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Longer titles found: Matrix multiplication algorithm (view), Computational complexity of matrix multiplication (view), Min-plus matrix multiplication (view)

searching for Matrix multiplication 200 found (492 total)

alternate case: matrix multiplication

Lie product formula (765 words) [view diff] no match in snippet view article find links to article

In mathematics, the Lie product formula, named for Sophus Lie (1875), but also widely called the Trotter product formula, named after Hale Trotter, states

Cache-oblivious algorithm (1,843 words) [view diff] exact match in snippet view article find links to article

a given cache. Optimal cache-oblivious algorithms are known for matrix multiplication, matrix transposition, sorting, and several other problems. Some

Global Arrays (461 words) [view diff] exact match in snippet view article find links to article

compatible with MPI. GA includes simple matrix computations (matrix-matrix multiplication, LU solve) and works with ScaLAPACK. Sparse matrices are available

Hill cipher (2,241 words) [view diff] exact match in snippet view article find links to article

matrix multiplication will result in large differences after the matrix multiplication. Indeed, some modern ciphers use a matrix multiplication step to

Henry Cohn (674 words) [view diff] exact match in snippet view article find links to article

with Chris Umans, Cohn initiated a group-theoretic approach to matrix multiplication, and is a core contributor to its continued development with various

Multilinear multiplication (3,861 words) [view diff] no match in snippet view article find links to article

In multilinear algebra, applying a map that is the tensor product of linear maps to a tensor is called a multilinear multiplication. Let F {\displaystyle

Communication-avoiding algorithm (1,680 words) [view diff] exact match in snippet view article find links to article

(\max(mkn/M^{1/2},mk+kn+mk))} . This lower bound is achievable by tiling matrix multiplication. More general results for other numerical linear algebra operations

ARM Neoverse (1,155 words) [view diff] no match in snippet view article find links to article

The ARM Neoverse is a group of 64-bit ARM processor cores licensed by Arm Holdings. The cores are intended for datacenter, edge computing, and high-performance

SuanShu numerical library (371 words) [view diff] exact match in snippet view article find links to article

parallel version of the adaptive strassen's algorithm for fast matrix multiplication. SuanShu has been quoted and used in a number of academic works

Triple product property (177 words) [view diff] exact match in snippet view article find links to article

research of fast matrix multiplication algorithms. Henry Cohn, Chris Umans. A Group-theoretic Approach to Fast Matrix Multiplication. arXiv:math.GR/0307321

Albert algebra (717 words) [view diff] exact match in snippet view article find links to article

{1}{2}}(x\cdot y+y\cdot x),} where ⋅ {\displaystyle \cdot } denotes matrix multiplication. Another is defined the same way, but using split octonions instead

JAX (software) (784 words) [view diff] exact match in snippet view article

below code demonstrates the pmap function's parallelization for matrix multiplication. # import pmap and random from JAX; import JAX NumPy from jax import

Logical matrix (1,989 words) [view diff] exact match in snippet view article find links to article

by inclusion; additionally it is a multiplicative lattice due to matrix multiplication. Every logical matrix in U corresponds to a binary relation. These

Alexander Munro Davie (918 words) [view diff] exact match in snippet view article find links to article

"some interest in applications of analysis to PDE, complexity of matrix multiplication and applications of mathematics to biology, particularly protein

Hierarchical matrix (2,149 words) [view diff] exact match in snippet view article find links to article

major advantage: the results of matrix arithmetic operations like matrix multiplication, factorization or inversion can be approximated in O ( n k α log

Multidimensional DSP with GPU acceleration (2,902 words) [view diff] exact match in snippet view article find links to article

unrolling the for-loop as shown in the following OpenCL example. // MxM matrix multiplication in C void matrixMul( float *A, // input matrix A float *B, // input

Tensor sketch (4,517 words) [view diff] exact match in snippet view article find links to article

{\displaystyle n^{2}d} using standard matrix multiplication techniques. The idea of Compressed Matrix Multiplication is the general identity X Y T = ∑ i

Triangle-free graph (2,524 words) [view diff] exact match in snippet view article find links to article

factors. Here ω {\displaystyle \omega } is the exponent of fast matrix multiplication; ω < 2.372 {\displaystyle \omega <2.372} from which it follows that

Widest path problem (3,017 words) [view diff] exact match in snippet view article find links to article

O(n(3+ω)/2) where ω is the exponent for fast matrix multiplication. Using the best known algorithms for matrix multiplication, this time bound becomes O(n2.688)

Strain partitioning (1,401 words) [view diff] exact match in snippet view article find links to article

strain throughout a deformed region. This effort is achieved through matrix multiplication. Refer to the figure below to conceptually visualize what is obtained

Janko group J2 (909 words) [view diff] exact match in snippet view article find links to article

})^{12}=1.} (Note that matrix multiplication on a finite field of order 4 is defined slightly differently from ordinary matrix multiplication. See Finite field

Two-port network (5,250 words) [view diff] exact match in snippet view article find links to article

allow the T-parameters of cascaded networks to be calculated by matrix multiplication of the component networks. T-parameters, like ABCD parameters, can

Apple A13 (667 words) [view diff] exact match in snippet view article find links to article

AMX blocks. Apple claims the AMX blocks are six times faster at matrix multiplication than the Apple A12's Vortex cores. The AMX blocks are capable of

Classical group (7,794 words) [view diff] exact match in snippet view article find links to article

space to make possible the representation of the group action as matrix multiplication from the left, just as for R and C. A form φ: V × V → F on some

Split-octonion (1,669 words) [view diff] exact match in snippet view article find links to article

nonassociative they cannot be represented by ordinary matrices (matrix multiplication is always associative). Zorn found a way to represent them as "matrices"

Machtey Award (179 words) [view diff] case mismatch in snippet view article find links to article

Size Problem with a Random Oracle" 2022 Robert Andrews (UIUC) "On Matrix Multiplication and Polynomial Identity Testing" 2021 Xiao Mao (MIT) "Breaking the

ELLA (programming language) (447 words) [view diff] exact match in snippet view article

ftp://ftp.dra.hmg.gb/pub/ella[dead link], public release. Code for matrix multiplication hardware design verification: MAC ZIP = ([INT n]TYPE t: vector1

Sun–Ni law (1,687 words) [view diff] exact match in snippet view article find links to article

determine the memory-bounded speedup of matrix multiplication. The memory requirement of matrix multiplication is roughly x = 3 N 2 {\displaystyle \textstyle

Lie algebra (10,477 words) [view diff] exact match in snippet view article find links to article

matrices with nonzero determinant), where the group operation is matrix multiplication. Likewise, g l ( n , C ) {\displaystyle {\mathfrak {gl}}(n,\mathbb

Quantum circuit (3,343 words) [view diff] exact match in snippet view article find links to article

architecture on-the-fly which make it a well suited tool to handle matrix multiplication. The main idea of accelerating quantum computing simulations is

Z-order curve (2,681 words) [view diff] exact match in snippet view article find links to article

an optimized index, the S2-geometry. The Strassen algorithm for matrix multiplication is based on splitting the matrices in four blocks, and then recursively

Riordan array (3,409 words) [view diff] exact match in snippet view article find links to article

Below are some often-used facts about Riordan arrays. Note that the matrix multiplication rules applied to infinite lower triangular matrices lead to finite

Pseudo-spectral method (2,505 words) [view diff] exact match in snippet view article find links to article

function V ( x ) {\displaystyle V(x)} transforms into a vector-matrix multiplication, which scales as N 2 {\displaystyle N^{2}} . Also, the matrix elements

Dual representation (1,699 words) [view diff] exact match in snippet view article find links to article

considered as column vectors so that the representation can act (by matrix multiplication) from the left. Given a basis for V and the dual basis for V*, the

Unitary matrix (1,331 words) [view diff] exact match in snippet view article find links to article

nonnegative integer n, the set of all n × n unitary matrices with matrix multiplication forms a group, called the unitary group U(n). Every square matrix

Apache SystemDS (983 words) [view diff] exact match in snippet view article find links to article

quantization for lossy compression, binary cell operations, left matrix multiplication. [experimental] New python bindings with supports for several builtins

Scene graph (2,230 words) [view diff] exact match in snippet view article find links to article

transformation group node would accumulate its transformation by matrix multiplication, vector displacement, quaternions or Euler angles. After which a

Matroid parity problem (3,443 words) [view diff] exact match in snippet view article find links to article

the exponent in the time bounds for fast matrix multiplication. In particular, using a matrix multiplication algorithm of Virginia Vassilevska Williams

Floyd–Warshall algorithm (3,071 words) [view diff] exact match in snippet view article find links to article

repeated Dijkstra approach. There are also known algorithms using fast matrix multiplication to speed up all-pairs shortest path computation in dense graphs

Generalized permutation matrix (899 words) [view diff] exact match in snippet view article find links to article

non-zero entries to lie in a group G, with the understanding that matrix multiplication will only involve multiplying a single pair of group elements, not

With high probability (383 words) [view diff] exact match in snippet view article find links to article

randomizations. Freivalds' algorithm: a randomized algorithm for verifying matrix multiplication. It runs faster than deterministic algorithms WHP. Treap: a randomized

Persistent homology (1,719 words) [view diff] exact match in snippet view article find links to article

fastest known algorithm for computing persistent homology runs in matrix multiplication time. Since the number of simplices is highly relevant for computation

JAMA (numerical linear algebra library) (245 words) [view diff] exact match in snippet view article

s.getU(); Matrix S = s.getS(); Matrix V = s.getV(); Example of matrix multiplication: Matrix result = A.times(B); List of numerical libraries JAMA :

Robert Kleinberg (333 words) [view diff] exact match in snippet view article find links to article

is known for his research work on group theoretic algorithms for matrix multiplication, online learning, network coding and greedy embedding, social networks

Row- and column-major order (2,316 words) [view diff] exact match in snippet view article find links to article

increased vulnerability to mistakes (forgetting to also invert matrix multiplication order, reverting to convention during code maintenance, etc.), but

List of things named after Jacques Hadamard (268 words) [view diff] exact match in snippet view article find links to article

Hadamard's embedding theorem [ru] Hadamard product: entry-wise matrix multiplication an infinite product expansion for the Riemann zeta function Hadamard

OjAlgo (283 words) [view diff] exact match in snippet view article find links to article

S = svd.getD(); MatrixStore<Double> V = svd.getQ2(); Example of matrix multiplication: PrimitiveDenseStore result = FACTORY.makeZero(matA.getRowDim()

Parallel algorithm (840 words) [view diff] exact match in snippet view article find links to article

addressed. Multiple-agent system (MAS) Parallel algorithms for matrix multiplication Parallel algorithms for minimum spanning trees Parallel computing

HPC Challenge Benchmark (695 words) [view diff] exact match in snippet view article find links to article

linear equations (global). DGEMM – measures performance for matrix-matrix multiplication (single, star). STREAM – measures sustained memory bandwidth to/from

Kazushige Goto (255 words) [view diff] case mismatch in snippet view article find links to article

Kazushige; van de Geijn, Robert A. (2008). "Anatomy of High-Performance Matrix Multiplication". ACM Transactions on Mathematical Software. 34 (3): 12:1–12:25

Group homomorphism (1,538 words) [view diff] exact match in snippet view article find links to article

|}a>0,b\in \mathbf {R} \right\}} forms a group under matrix multiplication. For any complex number u the function fu : G → C* defined by (

Four-vector (8,365 words) [view diff] exact match in snippet view article find links to article

entries, is given by X ′ = Λ X , {\displaystyle X'=\Lambda X,} (matrix multiplication) where the components of the primed object refer to the new frame

Diameter (graph theory) (1,082 words) [view diff] exact match in snippet view article

known matrix multiplication algorithms. For sparse graphs, with few edges, repeated breadth-first search is faster than matrix multiplication. Assuming

Abelian group (5,264 words) [view diff] exact match in snippet view article find links to article

because matrix multiplication is generally not commutative. However, some groups of matrices are abelian groups under matrix multiplication – one example

Jacobi identity (1,241 words) [view diff] exact match in snippet view article find links to article

the commutator, which measures the failure of commutativity in matrix multiplication. Instead of X × Y {\displaystyle X\times Y} , the Lie bracket notation

Efficient Java Matrix Library (387 words) [view diff] exact match in snippet view article find links to article

SimpleMatrix W = s.getW(); SimpleMatrix V = s.getV(); Example of matrix multiplication: SimpleMatrix result = matA.mult(matB); Use of a DecompositionFactory

Nilsemigroup (427 words) [view diff] exact match in snippet view article find links to article

nilsemigroup. The set of strictly upper triangular matrix, with matrix multiplication is nilpotent. Let I n = [ a , n ] {\displaystyle I_{n}=[a,n]} a

Non-negative matrix factorization (7,780 words) [view diff] exact match in snippet view article find links to article

W H . {\displaystyle \mathbf {V} =\mathbf {W} \mathbf {H} \,.} Matrix multiplication can be implemented as computing the column vectors of V as linear

Parallel Colt (217 words) [view diff] exact match in snippet view article find links to article

DoubleMatrix2D S = s.getS(); DoubleMatrix2D V = s.getV(); Example of matrix multiplication: DenseDoubleAlgebra alg = new DenseDoubleAlgebra(); DoubleMatrix2D

Matrix Toolkit Java (505 words) [view diff] exact match in snippet view article find links to article

following intrinsic operations: Matrix/vector multiplication. Matrix/matrix multiplication. Rank updates by matrices or vectors. Direct matrix solvers. The

Design matrix (1,591 words) [view diff] exact match in snippet view article find links to article

with the ith object. A regression model may be represented via matrix multiplication as y = X β + e , {\displaystyle y=X\beta +e,} where X is the design

Diagonalizable matrix (4,692 words) [view diff] exact match in snippet view article find links to article

\\0&0&\cdots &\lambda _{n}\end{bmatrix}}.} Performing the above matrix multiplication we end up with the following result: A [ α 1 α 2 ⋯ α n ] = [ λ 1

Klein four-group (1,384 words) [view diff] exact match in snippet view article find links to article

representation as 2 × 2 real matrices with the operation being matrix multiplication: e = ( 1 0 0 1 ) , a = ( 1 0 0 − 1 ) , {\displaystyle

Connection (vector bundle) (8,674 words) [view diff] exact match in snippet view article

s={\begin{pmatrix}s^{1}\\\vdots \\s^{k}\end{pmatrix}},} then using regular matrix multiplication one can write ∇ ( s ) = d s + A s {\displaystyle \nabla (s)=ds+As}

Involution (mathematics) (2,240 words) [view diff] exact match in snippet view article

there are natural examples that are not groups, for example square matrix multiplication (i.e. the full linear monoid) with transpose as the involution.

Eigenfunction (2,347 words) [view diff] exact match in snippet view article find links to article

\\c_{i}&=\sum _{j=1}^{n}b_{j}A_{ij}.\end{aligned}}} This is the matrix multiplication Ab = c written in summation notation and is a matrix equivalent

Expander code (2,562 words) [view diff] exact match in snippet view article find links to article

{\displaystyle R\,} corresponds to each column of P {\displaystyle P\,} . Matrix multiplication over GF ( 2 ) = { 0 , 1 } {\displaystyle {\text{GF}}(2)=\{0,1\}\

Rigid transformation (1,146 words) [view diff] exact match in snippet view article find links to article

this condition form a mathematical group under the operation of matrix multiplication called the orthogonal group of n×n matrices and denoted O(n). Compute

Timeline of algorithms (2,080 words) [view diff] exact match in snippet view article find links to article

integration developed by Robert Henry Risch 1969 – Strassen algorithm for matrix multiplication developed by Volker Strassen 1970 – Dinic's algorithm for computing

Lie group action (1,333 words) [view diff] exact match in snippet view article find links to article

{GL} (n,\mathbb {R} )} on R n {\displaystyle \mathbb {R} ^{n}} by matrix multiplication; more generally, any Lie group representation on a vector space;

Pilot ACE (1,347 words) [view diff] exact match in snippet view article find links to article

set of simultaneous equations, to invert a matrix, and to perform matrix multiplication. Though there was nothing new in this concept, where GIP was unique

Unipotent (1,826 words) [view diff] exact match in snippet view article find links to article

{\displaystyle a\mapsto {\begin{bmatrix}1&a\\0&1\end{bmatrix}}} Notice the matrix multiplication gives [ 1 a 0 1 ] ⋅ [ 1 b 0 1 ] = [ 1 a + b 0 1 ] {\displaystyle

Lie bracket of vector fields (1,956 words) [view diff] exact match in snippet view article find links to article

M_{n\times n}(\mathbb {R} )} , where ⋅ {\displaystyle \cdot } means matrix multiplication and I {\displaystyle I} is the identity matrix. The invariant vector

Circle group (2,078 words) [view diff] exact match in snippet view article find links to article

(}e^{i\theta _{2}}{\bigr )},} where × {\displaystyle \times } is matrix multiplication, the circle group is isomorphic to the special orthogonal group

Jblas: Linear Algebra for Java (368 words) [view diff] exact match in snippet view article find links to article

DoubleMatrix V = evd[0]; DoubleMatrix D = evd[1]; Example of matrix multiplication: DoubleMatrix result = matA.mmul(matB); Free and open-source software

H. T. Kung (955 words) [view diff] exact match in snippet view article find links to article

Linux kernel, and a communication-avoiding optimal distributed matrix multiplication algorithm. In 1992, Kung was appointed McKay professor of Electrical

Oseledets theorem (832 words) [view diff] exact match in snippet view article find links to article

specific ordering of the f(x(s)) values along the trajectory. Since matrix multiplication is, in general, not commutative, accumulation of multiplied cocycle

Multilinear subspace learning (1,550 words) [view diff] exact match in snippet view article find links to article

can be performed in N steps with each step performing a tensor-matrix multiplication (product). The N steps are exchangeable. This projection is an extension

Colt (libraries) (216 words) [view diff] exact match in snippet view article

DoubleMatrix2D S = s.getS(); DoubleMatrix2D V = s.getV(); Example of matrix multiplication: Algebra alg = new Algebra(); DoubleMatrix2D result = alg.mult(matA

Binary Goppa code (1,154 words) [view diff] exact match in snippet view article find links to article

{\displaystyle s(x)} can be used to produce such syndrome with a simple matrix multiplication. The algorithm then computes v ( x ) ≡ s ( x ) − 1 − x mod g ( x

Normal subgroup (3,157 words) [view diff] exact match in snippet view article find links to article

{\displaystyle n\times n} matrices with real entries under the operation of matrix multiplication and its subgroup S L n ( R ) {\displaystyle \mathrm {SL} _{n}(\mathbf

Multiplication (6,352 words) [view diff] exact match in snippet view article find links to article

inclusion of identity (the identity matrix) and inverses. However, matrix multiplication is not commutative, which shows that this group is non-abelian.

Polynomial evaluation (3,477 words) [view diff] exact match in snippet view article find links to article

{\displaystyle m^{3}} (or m 2.3 {\displaystyle m^{2.3}} using fast matrix multiplication). Matrix polynomials are important for example for computing the

Denavit–Hartenberg parameters (3,986 words) [view diff] exact match in snippet view article find links to article

is reversed. This is possible (despite the fact that in general, matrix multiplication is not commutative) since translations and rotations are concerned

Musical isomorphism (4,149 words) [view diff] exact match in snippet view article find links to article

{\displaystyle X^{\mu }=(ct,x,y,z)\,.} This operation is equivalent to the matrix multiplication ( − 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ) ( − c t x y z ) = ( c t x

Algebraic signal processing (1,547 words) [view diff] exact match in snippet view article find links to article

with composition (equivalent, in the finite-dimensional case, to matrix multiplication). For convenience, we write ρ a {\displaystyle \rho _{a}} for the

Pulse-coupled networks (851 words) [view diff] exact match in snippet view article find links to article

"A novel algorithm for all pairs shortest path problem based on matrix multiplication and pulse coupled neural network". Digital Signal Processing. 21

Morita equivalence (1,816 words) [view diff] exact match in snippet view article find links to article

then Xn is an Mn(R)-module where the module structure is given by matrix multiplication on the left of column vectors from X. This allows the definition

Cayley transform (2,249 words) [view diff] exact match in snippet view article find links to article

Q=(I-A)(I+A)^{-1}\,\!} produces an orthogonal matrix, Q (so that QTQ = I). The matrix multiplication in the definition of Q above is commutative, so Q can be alternatively

Hunter Monroe (637 words) [view diff] exact match in snippet view article find links to article

between computational problems with no fastest algorithm, such as matrix multiplication,. In theoretical physics, he has examined whether closed timelike

NumPy (2,460 words) [view diff] exact match in snippet view article find links to article

], [ 10.38136661, 8.44968437, 15.17639591]]) >>> np.dot(a, c) # matrix multiplication array([[ 53.61964114, 38.8741616 , 71.53462537], [ 118.4935668

Chainer (857 words) [view diff] exact match in snippet view article find links to article

the fixed connections between mathematical operations (such as matrix multiplication and nonlinear activations) in the network, and then run the actual

Unum (number format) (2,877 words) [view diff] exact match in snippet view article

maintained currently. Supports basic linear algebra functions in Julia (Matrix multiplication, Matrix solve, Elgen decomposition, etc.) PySigmoid Ken Mercado

Schur algebra (1,418 words) [view diff] exact match in snippet view article find links to article

\mathrm {GL} _{n}(k)} on V = k n {\displaystyle V=k^{n}} given by matrix multiplication). Schur algebras are "defined over the integers". This means that

Bfloat16 floating-point format (1,800 words) [view diff] exact match in snippet view article find links to article

truncation (round toward 0). Later on, when it becomes the input of matrix multiplication units, the conversion can have various rounding mechanisms depending

Bisection bandwidth (737 words) [view diff] exact match in snippet view article find links to article

algorithms for sorting, Fast Fourier transformation, and matrix-matrix multiplication become communication-limited—as opposed to CPU-limited or memory-limited—on

Total derivative (2,711 words) [view diff] exact match in snippet view article find links to article

Jacobian matrices, then the composite on the right-hand side is simply matrix multiplication. This is enormously useful in applications, as it makes it possible

Gram matrix (3,167 words) [view diff] exact match in snippet view article find links to article

\|}^{2}\geq 0.} The first equality follows from the definition of matrix multiplication, the second and third from the bi-linearity of the inner-product

Kernel (image processing) (1,718 words) [view diff] exact match in snippet view article

matrix operation being performed—convolution—is not traditional matrix multiplication, despite being similarly denoted by *. For example, if we have two

Isaac Nape (270 words) [view diff] exact match in snippet view article find links to article

quantum computing algorithms using reconfigurable optical vector-matrix multiplication Quantum searching algorithms using entangled structured light Self-learning

Affine connection (7,693 words) [view diff] exact match in snippet view article find links to article

Note that θ is also GL(n)-equivariant (where GL(n) acts on Rn by matrix multiplication). The pair (θ, ω) defines a bundle isomorphism of T(FM) with the

Lie algebra–valued differential form (1,555 words) [view diff] exact match in snippet view article find links to article

^{p+q}(M,{\mathfrak {g}})} are wedge products formed using the matrix multiplication on g {\displaystyle {\mathfrak {g}}} . Let f : g → h {\displaystyle

List of computer scientists (5,230 words) [view diff] exact match in snippet view article find links to article

Christopher Strachey – denotational semantics Volker Strassen – matrix multiplication, integer multiplication, Solovay–Strassen primality test Bjarne

Parsing expression grammar (6,505 words) [view diff] exact match in snippet view article find links to article

according to a general CFG is asymptotically equivalent to boolean matrix multiplication (thus likely between quadratic and cubic time). One classical example

TensorFlow (4,057 words) [view diff] exact match in snippet view article find links to article

July 24, 2017. Retrieved August 14, 2019. operations like sin, * (matrix multiplication), .* (element-wise multiplication), etc [..]. Compare to Python

Divide and conquer (disambiguation) (326 words) [view diff] exact match in snippet view article

eigenvalue algorithm, in mathematics Divide and conquer algorithm for matrix multiplication, in mathematics All pages with titles containing Divide and rule

Divide and conquer (disambiguation) (326 words) [view diff] exact match in snippet view article

eigenvalue algorithm, in mathematics Divide and conquer algorithm for matrix multiplication, in mathematics All pages with titles containing Divide and rule

Helmert transformation (1,329 words) [view diff] no match in snippet view article find links to article

order. The third step consists of the application of a rotation matrix, multiplication with the scale factor μ = 1 + s {\displaystyle \mu =1+s} (with a

Moment of inertia (17,179 words) [view diff] exact match in snippet view article find links to article

} . Note that the cross product can be equivalently written as matrix multiplication by combining the first operand and the operator into a skew-symmetric

Namespace (3,357 words) [view diff] exact match in snippet view article find links to article

last two characters (MM) showing what it actually does: matrix–matrix multiplication. It also has a few advantages: No special software tools are required

Modular exponentiation (2,802 words) [view diff] exact match in snippet view article find links to article

matrix exponentiation clearly extend to this context. The modular matrix multiplication C ≡ AB (mod n) is simply replaced everywhere by the group multiplication

CUR matrix approximation (975 words) [view diff] case mismatch in snippet view article find links to article

(2006-01-01). "Fast Monte Carlo Algorithms for Matrices I: Approximating Matrix Multiplication". SIAM Journal on Computing. 36 (1): 132–157. doi:10.1137/S0097539704442684

Transformer (deep learning architecture) (13,111 words) [view diff] exact match in snippet view article

encoding of the position n-steps-ahead or n-steps-behind, by a matrix multiplication. By taking a linear sum, any convolution can also be implemented

Levenberg–Marquardt algorithm (3,211 words) [view diff] exact match in snippet view article find links to article

(size of the vector β {\displaystyle {\boldsymbol {\beta }}} ). The matrix multiplication ( J T J ) {\displaystyle \left(\mathbf {J} ^{\mathrm {T} }\mathbf

Key selection vector (963 words) [view diff] exact match in snippet view article find links to article

the given system (i.e. getting a key from a KSV can be viewed as matrix multiplication), someone could determine the Device Key Set matrix from any 40-50

Homogeneous coordinates (3,958 words) [view diff] exact match in snippet view article find links to article

geometric transformations can be combined with this and each other by matrix multiplication. As a result, any perspective projection of space can be represented

Asymptotically optimal algorithm (965 words) [view diff] exact match in snippet view article find links to article

resolved either way. Coppersmith and Winograd (1982) proved that matrix multiplication has a weak form of speed-up among a restricted class of algorithms

Advanced Encryption Standard (5,675 words) [view diff] exact match in snippet view article find links to article

j}\\a_{1,j}\\a_{2,j}\\a_{3,j}\end{bmatrix}}\qquad 0\leq j\leq 3} Matrix multiplication is composed of multiplication and addition of the entries. Entries

XOR swap algorithm (2,011 words) [view diff] exact match in snippet view article find links to article

results. The sequence of operations in AddSwap can be expressed via matrix multiplication as: ( 1 − 1 0 1 ) ( 1 0 1 − 1 ) ( 1 1 0 1 ) = ( 0 1 1 0 ) {\displaystyle

Richardson–Lucy deconvolution (2,155 words) [view diff] exact match in snippet view article find links to article

x {\displaystyle \mathbf {E} =\mathbf {H} \mathbf {x} } where a matrix multiplication is implied. This can also be written in the form E m = ∑ n K H m

Janko group J3 (2,043 words) [view diff] exact match in snippet view article find links to article

list are 18x18 matrices over the finite field of order 9, with matrix multiplication carried out with finite field arithmetic: ( 0 8 0 0 0 0 0 0 0 0

Bulk synchronous parallel (2,109 words) [view diff] exact match in snippet view article find links to article

Springer-Verlag pp.46-61 (1995) [2] W F McColl and A Tiskin. Memory-efficient matrix multiplication in the BSP model. Algorithmica 24(3) pp.287-297 (1999) [3] J M D

VSOP model (2,020 words) [view diff] exact match in snippet view article find links to article

and rotations (e.g. ecliptic to equatorial coordinates) through matrix multiplication. VSOP87 comes in six tables: VSOP87 Heliocentric ecliptic orbital

Softmax function (5,279 words) [view diff] exact match in snippet view article find links to article

queries and keys per loop iteration, in a similar way as blocked matrix multiplication. If backpropagation is needed, then the output vectors and the intermediate

Mersenne Twister (3,995 words) [view diff] exact match in snippet view article find links to article

multiplication by A can be efficiently expressed as: (remember that here matrix multiplication is being done in F 2 {\displaystyle {\textbf {F}}_{2}} , and therefore

Monster group (2,990 words) [view diff] exact match in snippet view article find links to article

field of order 2) which together generate the monster group by matrix multiplication; this is one dimension lower than the 196,883-dimensional representation

PostBQP (3,635 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \pi _{0}} . In order to do this, we expand the definition of matrix multiplication: Ψ ω = ∑ α 1 , … , α G A ω , α G G A α G , α G − 1 G − 1 ⋯ A α 3

Scattering parameters (7,532 words) [view diff] exact match in snippet view article find links to article

}\end{pmatrix}}{\begin{pmatrix}T_{3}\end{pmatrix}}\,} Note that matrix multiplication is not commutative, so the order is important. As with S-parameters

PostBQP (3,635 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \pi _{0}} . In order to do this, we expand the definition of matrix multiplication: Ψ ω = ∑ α 1 , … , α G A ω , α G G A α G , α G − 1 G − 1 ⋯ A α 3

Attention (machine learning) (3,524 words) [view diff] exact match in snippet view article

fully-connected weight matrix. ⊕, ⊗ ⊕, vector concatenation; ⊗, matrix multiplication. corr Column-wise softmax(matrix of all combinations of dot products)

Linear differential equation (4,754 words) [view diff] exact match in snippet view article find links to article

equations, but with complications stemming from noncommutativity of matrix multiplication. Let u ′ = A u . {\displaystyle \mathbf {u} '=A\mathbf {u} .} be

Shmuel Friedland (857 words) [view diff] exact match in snippet view article find links to article

Zhang and Lek-Heng Lim: "Grothendieck constant is norm of Strassen matrix multiplication tensor", arXiv preprint arXiv:1711.04427, 2017. (See Grothendieck

Digital image processing (5,364 words) [view diff] exact match in snippet view article find links to article

third dimension, i.e. the constant 1, allows translation. Because matrix multiplication is associative, multiple affine transformations can be combined

List of named matrices (1,336 words) [view diff] case mismatch in snippet view article find links to article

matrix Mathematics portal Hogben 2006, Ch. 31.3. Weisstein, Eric W. "Matrix Multiplication". mathworld.wolfram.com. Retrieved 2020-09-07. "Non-derogatory matrix

Pseudovector (4,332 words) [view diff] exact match in snippet view article find links to article

concrete example is that of row and column vectors under the usual matrix multiplication operator: in one order they yield the dot product, which is just

Anyon (5,252 words) [view diff] exact match in snippet view article find links to article

dimension, then these linear transformations need not commute (just as matrix multiplication does not). Gregory Moore, Nicholas Read, and Xiao-Gang Wen pointed

Pushmeet Kohli (1,068 words) [view diff] exact match in snippet view article find links to article

reinforcement learning agent that found new efficient algorithms for matrix multiplication SynthID - system for watermarking AI generated images. AlphaMissense

Conjunctive grammar (1,396 words) [view diff] exact match in snippet view article find links to article

Cocke-Kasami-Younger, as well as Valiant's algorithm running as fast as matrix multiplication. A property that is undecidable already for context-free languages

Octonion (5,316 words) [view diff] exact match in snippet view article find links to article

Using a slightly modified (non-associative) quaternionic matrix multiplication: [ α 0 α 1 α 2 α 3 ] ∘ [ β 0 β 1 β 2 β 3 ] = [ α 0 β 0 + β 2 α 1

Knuth's up-arrow notation (3,370 words) [view diff] no match in snippet view article find links to article

b)=a+b=&a+\underbrace {1+1+\dots +1} \\&b{\mbox{ copies of }}1\end{matrix}}} Multiplication by a natural number is defined as iterated addition: H 2 ( a ,

Vandermonde matrix (5,263 words) [view diff] exact match in snippet view article find links to article

… , x m {\displaystyle x=x_{0},\ x_{1},\dots ,\ x_{m}} via a matrix multiplication V a = y {\displaystyle Va=y} , where a = ( a 0 , … , a n ) {\displaystyle

Letter case (7,202 words) [view diff] exact match in snippet view article find links to article

conventions make this possible. So for example, a function dealing with matrix multiplication might formally be called: SGEMM(*), with the asterisk standing in

Graphics processing unit (8,446 words) [view diff] exact match in snippet view article find links to article

since they have significant FLOPS performance increases, using 4×4 matrix multiplication and division, resulting in hardware performance up to 128 TFLOPS

Optimizing compiler (5,417 words) [view diff] exact match in snippet view article find links to article

loop. Loop nest optimization Some pervasive algorithms such as matrix multiplication have very poor cache behavior and excessive memory accesses. Loop

Private biometrics (4,559 words) [view diff] exact match in snippet view article find links to article

one-way, fully homomorphic, Euclidean-measurable feature vector using matrix multiplication from the neural network that may then be stored locally or transmitted

Yield curve (5,739 words) [view diff] exact match in snippet view article find links to article

discount factor function P we should have that F = AP (this is a matrix multiplication). Actually, noise in the financial markets means it is not possible

Type system (7,205 words) [view diff] exact match in snippet view article find links to article

We can then define typing rules such as the following rule for matrix multiplication: m a t r i x m u l t i p l y : m a t r i x ( k , m ) × m a t r i

Convolution (8,819 words) [view diff] case mismatch in snippet view article find links to article

Wang, Lingli (May 2021). "SWM: A High-Performance Sparse-Winograd Matrix Multiplication CNN Accelerator". IEEE Transactions on Very Large Scale Integration

SequenceL (2,395 words) [view diff] exact match in snippet view article find links to article

their implementation. For example, the mathematical definition of matrix multiplication is as follows: The product of the m×p matrix A with the p×n matrix

Residual neural network (2,977 words) [view diff] exact match in snippet view article find links to article

The function F ( x ) {\displaystyle F(x)} is often represented by matrix multiplication interlaced with activation functions and normalization operations

CUDA (4,133 words) [view diff] exact match in snippet view article find links to article

1)) print(dest - a * b) Additional Python bindings to simplify matrix multiplication operations can be found in the program pycublas. import numpy from

Wave packet (5,959 words) [view diff] exact match in snippet view article find links to article

x')=K_{t}(x-x')\,.} Translation invariance means that continuous matrix multiplication, C ( x , x ″ ) = ∫ x ′ A ( x , x ′ ) B ( x ′ , x ″ ) , {\displaystyle

Wave packet (5,959 words) [view diff] exact match in snippet view article find links to article

x')=K_{t}(x-x')\,.} Translation invariance means that continuous matrix multiplication, C ( x , x ″ ) = ∫ x ′ A ( x , x ′ ) B ( x ′ , x ″ ) , {\displaystyle

Tensor (9,357 words) [view diff] exact match in snippet view article find links to article

arrangement of transposed vectors and by applying the rules of matrix multiplication, but the tensor product should not be confused with this. There

Moduli stack of elliptic curves (2,344 words) [view diff] exact match in snippet view article find links to article

n)\mapsto (m,n)\cdot {\begin{pmatrix}a&b\\c&d\end{pmatrix}}} which is matrix multiplication on the right, so ( m , n ) ⋅ ( a b c d ) = ( a m + c n , b m + d

Projective plane (6,933 words) [view diff] exact match in snippet view article find links to article

notation. The points are viewed as row vectors, so to make the matrix multiplication work in this expression, the point x must be written as a column

Cell (processor) (7,391 words) [view diff] exact match in snippet view article

of their theoretical peak performance running optimized parallel matrix multiplication. Toshiba has developed a co-processor powered by four SPEs, but

Representation theory of the Lorentz group (19,763 words) [view diff] exact match in snippet view article find links to article

Weyl group are considered as orthogonal transformations, acting by matrix multiplication, on the real vector space of roots. If −I is an element of the Weyl

Salman A. Avestimehr (1,224 words) [view diff] case mismatch in snippet view article find links to article

“Polynomial Codes: an Optimal Design for High-Dimensional Coded Matrix Multiplication,” in NIPS, 2017. C. Geng, N. Naderializadeh, A. S. Avestimehr, and

APL syntax and symbols (3,502 words) [view diff] exact match in snippet view article find links to article

is an inner product. An inner product intended for conventional matrix multiplication uses the + and × functions, replacing these with other dyadic functions

English Electric DEUCE (3,228 words) [view diff] exact match in snippet view article find links to article

codewords would be written to use the bricks to perform such tasks as: matrix multiplication; matrix inversion; term-by-term matrix arithmetic (addition, subtraction

The Vectors of Mind (1,996 words) [view diff] exact match in snippet view article find links to article

Mathematical Introduction. A brief presentation of matrices, determinants, matrix multiplication, diagonal matrices, the inverse, the characteristic equation, summation

Vector processor (8,675 words) [view diff] case mismatch in snippet view article find links to article

Videocore IV QPU analysis by Jeff Bush "Coding for Neon - Part 3 Matrix Multiplication". 11 September 2013. SIMD considered harmful ARM SVE2 tutorial "Sse

Permutation (11,671 words) [view diff] exact match in snippet view article find links to article

otherwise. Since composition of linear mappings is described by matrix multiplication, it follows that this construction is compatible with composition

Transfer function matrix (3,178 words) [view diff] exact match in snippet view article find links to article

cases the overall transmission parameters are found simply by the matrix multiplication of the transmission parameter matrices of the constituent components

Eckart conditions (3,346 words) [view diff] exact match in snippet view article find links to article

^{\mathrm {int} })^{\mathrm {T} }.} By using the rules for block matrix multiplication we can show that ( B T ) − 1 M B − 1 = ( G − 1 0 0 N − 1 ) , {\displaystyle

Iterative proportional fitting (3,463 words) [view diff] exact match in snippet view article find links to article

same as classical IPF. In practice, one would not implement actual matrix multiplication with the whole R and S matrices; the RAS form is more a notational

Petri net (7,238 words) [view diff] exact match in snippet view article find links to article

W^{T}=-W^{-}+W^{+}} can be used to describe the reachable markings in terms of matrix multiplication, as follows. For any sequence of transitions w, write o ( w ) {\displaystyle

Chernoff bound (5,089 words) [view diff] case mismatch in snippet view article find links to article

(2011). "Low Rank Matrix-Valued Chernoff Bounds and Approximate Matrix Multiplication". arXiv:1005.2724 [cs.DM]. Goldberg, A. V.; Hartline, J. D. (2001)

Neural network Gaussian process (2,964 words) [view diff] exact match in snippet view article find links to article

architecture: Generally, if an architecture can be expressed solely via matrix multiplication and coordinatewise nonlinearities (i.e., a tensor program), then

Llama.cpp (1,244 words) [view diff] exact match in snippet view article find links to article

on GitHub. In March 2024 Justine Tunney introduced new optimized matrix multiplication kernels for x86 and ARM CPUs, improving prompt evaluation performance

Bispinor (3,655 words) [view diff] exact match in snippet view article find links to article

introduce any 4-dimensional complex vector space U where the γμ act by matrix multiplication. Here U = C4 will do nicely. Let Λ = eωμνMμν be a Lorentz transformation

Gauge covariant derivative (4,484 words) [view diff] exact match in snippet view article find links to article

}U^{-1}} . Further, (suppressing indices and replacing them by matrix multiplication) if D μ = ∂ μ − i g A μ {\displaystyle D_{\mu }=\partial _{\mu }-igA_{\mu

Matrix mechanics (10,615 words) [view diff] exact match in snippet view article find links to article

_{k=0}^{\infty }X_{mk}P_{kn}.} Born pointed out that this is the law of matrix multiplication, so that the position, the momentum, the energy, all the observable

Model compression (1,145 words) [view diff] exact match in snippet view article find links to article

to represent W {\displaystyle W} approximately, and accelerates matrix multiplication by W {\displaystyle W} . Low-rank approximations can be found by

Symmetry in quantum mechanics (7,915 words) [view diff] exact match in snippet view article find links to article

is Abelian since one-dimensional matrices always commute under matrix multiplication. Lagrangians in quantum field theory for complex scalar fields are

Direct-quadrature-zero transformation (4,674 words) [view diff] exact match in snippet view article find links to article

for Clarke's original transformation. It is easy to verify (by matrix multiplication) that the inverse of KC is K C − 1 = [ 2 6 0 1 3 − 1 6 1 2 1 3 −

Path integral formulation (14,277 words) [view diff] exact match in snippet view article find links to article

{\displaystyle e^{-ipq(t)},} and if this is also interpreted as a matrix multiplication, the sum over all states integrates over all q(t), and so it takes

Gamma matrices (7,254 words) [view diff] exact match in snippet view article find links to article

below). The Clifford algebra is assumed to act on Ux as well (by matrix multiplication with column vectors Ψ(x) in Ux for all x). This will be the primary

Yefim Dinitz (1,490 words) [view diff] exact match in snippet view article find links to article

Mikhail Kronrod, Arlazarov, and Faradjev published the Boolean matrix multiplication algorithm that would make them famous as the "Four Russians". Adelson-Velsky

Zhegalkin polynomial (5,153 words) [view diff] exact match in snippet view article find links to article

2^{3}} . It can be proven through mathematical induction and block-matrix multiplication that any such "Sierpiński matrix" S n {\displaystyle S_{n}} is its

Tensor operator (9,012 words) [view diff] exact match in snippet view article find links to article

{\displaystyle {D(R)}_{m'm}^{(j)}=\langle j,m'|U(R)|j,m\rangle } gives the matrix multiplication: | ψ ¯ ⟩ = ∑ m m ′ c j m D m ′ m ( j ) | j , m ′ ⟩ ⇒ | ψ ¯ ⟩ = D

List of numerical analysis topics (8,335 words) [view diff] exact match in snippet view article find links to article

whose successive powers approach the zero matrix Algorithms for matrix multiplication: Strassen algorithm Coppersmith–Winograd algorithm Cannon's algorithm

Twin-width (4,077 words) [view diff] exact match in snippet view article find links to article

Stéphan (2023), "Twin-width V: linear minors, modular counting, and matrix multiplication", in Berenbrink, Petra; Bouyer, Patricia; Dawar, Anuj; Kanté, Mamadou

Intrinsic bond orbitals (2,927 words) [view diff] exact match in snippet view article find links to article

{\displaystyle U_{ii'}} , which produces the localized IBOs upon matrix multiplication with set of occupied MOs | i ⟩ {\displaystyle |i\rangle } , is thereby

Matrix Chernoff bound (4,957 words) [view diff] case mismatch in snippet view article find links to article

(2010). "Low-Rank Matrix-valued Chernoff Bounds and Approximate Matrix Multiplication". arXiv:1005.2724 [cs.DS]. Oliveira, R.I. (2010a). "Concentration

Knowledge graph embedding (5,953 words) [view diff] exact match in snippet view article find links to article

(Obama,president\_of,USA)} , Obama is a person and USA is a country. Matrix multiplication is an expensive procedure in TransR to compute the projection. In

Computation of cyclic redundancy checks (5,698 words) [view diff] exact match in snippet view article find links to article

(y_{i-1}\oplus x_{i}).} The implementation challenge is that the matrix multiplication by A r {\displaystyle A^{r}} must be performed in r {\displaystyle

Angular velocity tensor (2,523 words) [view diff] exact match in snippet view article find links to article

Substituting ω for Ω into the above velocity expression, and replacing matrix multiplication by an equivalent cross product: V i = V + ω × r i {\displaystyle

Wigner rotation (6,413 words) [view diff] exact match in snippet view article find links to article

not v then u. Performing the Lorentz transformations by block matrix multiplication, X ″ = B ( v ) X ′ , X ′ = B ( u ) X ⇒ X ″ = Λ X {\displaystyle

List of women in mathematics (23,272 words) [view diff] exact match in snippet view article find links to article

Williams, Bulgarian-American researcher on graph algorithms and fast matrix multiplication Stephanie van Willigenburg, Canadian researcher in algebraic combinatorics

Tesla Dojo (2,755 words) [view diff] exact match in snippet view article find links to article

two-way SMT, which feeds either a 64-byte SIMD unit or four 8×8×4 matrix multiplication units. The network on-chip (NOC) router links cores into a two-dimensional

Mathematics education in the United States (12,483 words) [view diff] exact match in snippet view article find links to article

functions, logarithms, systems of linear equations, matrices (including matrix multiplication, 2 × 2 {\displaystyle 2\times 2} matrix determinants, Cramer's rule

CPUID (12,982 words) [view diff] case mismatch in snippet view article find links to article

CPUID EAX=24h, ECX=1: Discrete AVX10 features in ECX Bit ECX Short Feature 0 (VPMM) (Vector-Extension Packed Matrix Multiplication) 31:1 (reserved)

Discrete Universal Denoiser (4,987 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \left(\mathbf {a} \odot \mathbf {b} \right)_{i}=a_{i}b_{i}} . Matrix multiplication is evaluated before the Schur product, so that Π − ⊤ μ ⊙ π z {\displaystyle

Representation theory of finite groups (21,294 words) [view diff] exact match in snippet view article find links to article

\,{\text{ is an upper triangular matrix}}\}.} Together with the matrix multiplication G {\displaystyle G} is an infinite group. G {\displaystyle G} acts

Fortran 95 language features (9,442 words) [view diff] exact match in snippet view article find links to article

DOT_PRODUCT Dot product of 2 rank-one arrays MATMUL Matrix multiplication

Symmetry of diatomic molecules (7,820 words) [view diff] exact match in snippet view article find links to article

represented as matrices, so that the group operation becomes the ordinary matrix multiplication. In quantum mechanics, the evolution of an arbitrary superposition

Llama (language model) (4,940 words) [view diff] exact match in snippet view article

single executable file. Tunney et al. introduced new optimized matrix multiplication kernels for x86 and ARM CPUs, improving prompt evaluation performance

Universal multiport interferometer (4,174 words) [view diff] exact match in snippet view article find links to article

}\end{bmatrix}}.} Repeating this step in a recursive fashion until the matrix multiplication involves T ( 2 , 1 ) ( ω 2 , 1 , ϕ 2 , 1 ) {\textstyle T_{(2,1)}(\omega