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Longer titles found: Matrix representation of Maxwell's equations (view), Matrix representation of conic sections (view)

searching for Matrix representation 189 found (217 total)

alternate case: matrix representation

Complex number (11,795 words) [view diff] exact match in snippet view article find links to article

(w)\end{pmatrix}},} that is, the one mentioned in the section on matrix representation of complex numbers above. While this is a linear representation

Symmetric bilinear form (1,511 words) [view diff] exact match in snippet view article find links to article

&e_{n}\end{bmatrix}}S} with S an invertible n×n matrix. Now the new matrix representation for the symmetric bilinear form is given by A ′ = S T A S . {\displaystyle

Translation (geometry) (1,720 words) [view diff] no match in snippet view article

In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction

Quaternion (12,648 words) [view diff] exact match in snippet view article find links to article

produces a diagonal complex matrix representation of complex numbers, and setting b = d = 0 produces a real matrix representation. The norm of a quaternion

Sesquilinear form (2,832 words) [view diff] exact match in snippet view article find links to article

V , h ) {\displaystyle (V,h)} is called a Hermitian space. The matrix representation of a complex Hermitian form is a Hermitian matrix. A complex Hermitian

Scaling (geometry) (1,609 words) [view diff] no match in snippet view article

In affine geometry, uniform scaling (or isotropic scaling) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale

Dual number (2,780 words) [view diff] no match in snippet view article find links to article

In algebra, the dual numbers are a hypercomplex number system first introduced in the 19th century. They are expressions of the form a + bε, where a and

Orthogonal transformation (727 words) [view diff] exact match in snippet view article find links to article

generalized to higher dimensions. In finite-dimensional spaces, the matrix representation (with respect to an orthonormal basis) of an orthogonal transformation

Module homomorphism (2,467 words) [view diff] exact match in snippet view article find links to article

{\displaystyle F\simeq R^{n}} . The above procedure then gives the matrix representation with respect to such choices of the bases. For more general modules

Dihedral group (3,499 words) [view diff] no match in snippet view article find links to article

In mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections. Dihedral groups are among the

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

Aff(Fp) has p irreducible representations. By above paragraph (§ Matrix representation), there exist p − 1 one-dimensional representations, decided by

Algebra of physical space (1,560 words) [view diff] exact match in snippet view article find links to article

units such that c = 1 are used, called natural units. In the Pauli matrix representation, the unit basis vectors are replaced by the Pauli matrices and the

Supertree (1,040 words) [view diff] case mismatch in snippet view article find links to article

data. The most well known method for supertree construction is Matrix Representation with Parsimony (MRP), in which the input source trees are represented

Additive category (1,571 words) [view diff] no match in snippet view article find links to article

In mathematics, specifically in category theory, an additive category is a preadditive category C admitting all finitary biproducts. There are two equivalent

Applications of dual quaternions to 2D geometry (1,473 words) [view diff] no match in snippet view article find links to article

In this article, certain applications of the dual quaternion algebra to 2D geometry are discussed. At this present time, the article is focused on a 4-dimensional

Blocking (statistics) (2,842 words) [view diff] no match in snippet view article

In the statistical theory of the design of experiments, blocking is the arranging of experimental units that are similar to one another in groups (blocks)

Vector projection (1,720 words) [view diff] no match in snippet view article find links to article

The vector projection (also known as the vector component or vector resolution) of a vector a on (or onto) a nonzero vector b is the orthogonal projection

Projection (linear algebra) (5,806 words) [view diff] no match in snippet view article

In linear algebra and functional analysis, a projection is a linear transformation P {\displaystyle P} from a vector space to itself (an endomorphism)

Quaternionic representation (689 words) [view diff] exact match in snippet view article find links to article

quaternion-linear transformations of V. In particular, a quaternionic matrix representation of g assigns a square matrix of quaternions ρ(g) to each element

Local regression (5,124 words) [view diff] exact match in snippet view article find links to article

} is a vector of the responses Y i {\displaystyle Y_{i}} . This matrix representation is crucial for studying the theoretical properties of local regression

Generalized Clifford algebra (1,695 words) [view diff] exact match in snippet view article find links to article

_{jk}^{N_{k}}\,} ∀ j,k,ℓ,m = 1, . . . ,n. Moreover, in any irreducible matrix representation, relevant for physical applications, it is required that ω j k =

Generalised circle (1,131 words) [view diff] no match in snippet view article find links to article

In geometry, a generalized circle, sometimes called a cline or circline, is a straight line or a circle, the curves of constant curvature in the Euclidean

Lamplighter group (884 words) [view diff] no match in snippet view article find links to article

In mathematics, the lamplighter group L of group theory is the restricted wreath product Z 2 ≀ Z {\displaystyle \mathbf {Z} _{2}\wr \mathbf {Z} } . The

Creation and annihilation operators (4,463 words) [view diff] no match in snippet view article find links to article

Creation operators and annihilation operators are mathematical operators that have widespread applications in quantum mechanics, notably in the study of

Social accounting matrix (1,486 words) [view diff] exact match in snippet view article find links to article

within an economy (regional or national). It is at the core, a matrix representation of the national accounts for a given country, but can be extended

Octonion (5,316 words) [view diff] no match in snippet view article find links to article

In mathematics, the octonions are a normed division algebra over the real numbers, a kind of hypercomplex number system. The octonions are usually represented

Higher-dimensional gamma matrices (3,664 words) [view diff] exact match in snippet view article find links to article

including the C, P and T symmetries do not require a specific matrix representation, and one obtains a clearer definition of chirality in this way.

Set balancing (864 words) [view diff] no match in snippet view article find links to article

The set balancing problem in mathematics is the problem of dividing a set to two subsets that have roughly the same characteristics. It arises naturally

SimRank (2,573 words) [view diff] no match in snippet view article find links to article

SimRank is a general similarity measure, based on a simple and intuitive graph-theoretic model. SimRank is applicable in any domain with object-to-object

Karush–Kuhn–Tucker conditions (3,966 words) [view diff] no match in snippet view article find links to article

In mathematical optimization, the Karush–Kuhn–Tucker (KKT) conditions, also known as the Kuhn–Tucker conditions, are first derivative tests (sometimes

Paravector (4,422 words) [view diff] exact match in snippet view article find links to article

_{21}-\psi _{12}^{*}&\psi _{22}-\psi _{22}^{*}\end{pmatrix}}} The matrix representation of a Euclidean space in higher dimensions can be constructed in

Barnsley fern (1,329 words) [view diff] exact match in snippet view article find links to article

removal of the section which includes the bottom two leaves. In the matrix representation, it can be seen to be a slight clockwise rotation, scaled to be

Irreducible representation (2,824 words) [view diff] exact match in snippet view article find links to article

into a set of invertible matrices and in this context is called a matrix representation. However, it simplifies things greatly if we think of the space

Givens rotation (3,246 words) [view diff] exact match in snippet view article find links to article

however, a Givens rotation is simply a matrix as defined in the Matrix representation section above and does not necessarily respect the right-hand rule

Kinematics (9,219 words) [view diff] no match in snippet view article find links to article

In physics, kinematics studies the geometrical aspects of motion of physical objects independent of forces that set them in motion. Constrained motion

Parity (physics) (5,164 words) [view diff] exact match in snippet view article

powerful controlling principle underlying quantum transitions. A matrix representation of P (in any number of dimensions) has determinant equal to −1,

Closure with a twist (1,557 words) [view diff] exact match in snippet view article find links to article

string. A matrix representation of a cwatset is formed by writing its words as the rows of a 0-1 matrix. For instance a matrix representation of F is given

Conway polyhedron notation (2,673 words) [view diff] no match in snippet view article find links to article

In geometry and topology, Conway polyhedron notation, invented by John Horton Conway and promoted by George W. Hart, is used to describe polyhedra based

Inductance (8,766 words) [view diff] no match in snippet view article find links to article

Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The electric current produces a magnetic

Inductance (8,766 words) [view diff] no match in snippet view article find links to article

Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The electric current produces a magnetic

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

this column vector has finite dimension. Additionally, define a matrix representation of the linear operator D with elements A i j = ⟨ u i , D u j ⟩ =

Leslie matrix (1,224 words) [view diff] exact match in snippet view article find links to article

{\displaystyle n_{x+1}=s_{x}n_{x}} . This implies the following matrix representation: [ n 0 n 1 ⋮ n ω − 1 ] t + 1 = [ f 0 f 1 f 2 … f ω − 2 f ω − 1 s

3-sphere (4,048 words) [view diff] exact match in snippet view article find links to article

parallelizable are S1, S3, and S7. By using a matrix representation of the quaternions, H, one obtains a matrix representation of S3. One convenient choice is given

Dirac algebra (2,342 words) [view diff] exact match in snippet view article find links to article

in developing the Dirac equation for spin-⁠1/2⁠ particles with a matrix representation of the gamma matrices, which represent the generators of the algebra

The Product Space (2,618 words) [view diff] no match in snippet view article find links to article

The Product Space is a network that formalizes the idea of relatedness between products traded in the global economy. The network first appeared in the

Clifford gates (950 words) [view diff] exact match in snippet view article find links to article

powers of 1 / 2 {\displaystyle {1}/{\sqrt {2}}} in the unitary matrix representation, removing the phase gate S disallows i {\displaystyle i} in the

Symmetric relation (385 words) [view diff] exact match in snippet view article find links to article

count the symmetric relations on n elements, that in their binary matrix representation the upper right triangle determines the relation fully, and it can

Rijndael MixColumns (2,930 words) [view diff] no match in snippet view article find links to article

The MixColumns operation performed by the Rijndael cipher or Advanced Encryption Standard is, along with the ShiftRows step, its primary source of diffusion

Permutation (11,671 words) [view diff] no match in snippet view article find links to article

In mathematics, a permutation of a set can mean one of two different things: an arrangement of its members in a sequence or linear order, or the act or

Bilinear form (2,726 words) [view diff] exact match in snippet view article find links to article

other vector. A vector v, with matrix representation x, is in the radical of a bilinear form with matrix representation A, if and only if Ax = 0 ⇔ xTA

Hooke's law (9,420 words) [view diff] no match in snippet view article find links to article

In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly

Binary relation (8,830 words) [view diff] no match in snippet view article find links to article

In mathematics, a binary relation associates some elements of one set called the domain with some elements of another set called the codomain. Precisely

Spinor (9,924 words) [view diff] exact match in snippet view article find links to article

on which these matrices act are spinors. However, the particular matrix representation of the Clifford algebra, hence what precisely constitutes a "column

Essential matrix (3,215 words) [view diff] exact match in snippet view article find links to article

as: where [ t ] × {\displaystyle [\mathbf {t} ]_{\times }} is the matrix representation of the cross product with t {\displaystyle \mathbf {t} } . Note:

Design structure matrix (1,635 words) [view diff] exact match in snippet view article find links to article

industries, to name a few, as well as in many government agencies. The matrix representation has several strengths. The matrix can represent a large number of

Character (mathematics) (699 words) [view diff] exact match in snippet view article

definition would be equivalent to the above (For abelian groups, every matrix representation decomposes into a direct sum of 1 × 1 {\displaystyle 1\times 1}

Diffusion wavelets (1,026 words) [view diff] exact match in snippet view article find links to article

[ Φ b ] Φ a {\displaystyle [\Phi _{b}]_{\Phi _{a}}} denotes the matrix representation of the scaling basis Φ b {\displaystyle \Phi _{b}} represented with

Affine transformation (3,603 words) [view diff] exact match in snippet view article find links to article

matrix A {\displaystyle A} appearing in its matrix representation is invertible. The matrix representation of the inverse transformation is thus [ A −

Adjacency list (1,190 words) [view diff] exact match in snippet view article find links to article

adjacency list representation occupies more space than the adjacency matrix representation when d > 1/64. Thus a graph must be sparse enough to justify an

Complex conjugate (1,856 words) [view diff] case mismatch in snippet view article find links to article

Wirtinger derivatives – Concept in complex analysis "Lesson Explainer: Matrix Representation of Complex Numbers | Nagwa". www.nagwa.com. Retrieved 2023-01-04

Quaternions and spatial rotation (11,740 words) [view diff] no match in snippet view article find links to article

Unit quaternions, known as versors, provide a convenient mathematical notation for representing spatial orientations and rotations of elements in three

Generalized eigenvector (7,057 words) [view diff] exact match in snippet view article find links to article

n} -dimensional vector space and let A {\displaystyle A} be the matrix representation of a linear map from V {\displaystyle V} to V {\displaystyle V}

Jones calculus (4,069 words) [view diff] case mismatch in snippet view article find links to article

2248B. doi:10.1364/JOSAA.10.002248. Fymat, A. L. (1971). "Jones's Matrix Representation of Optical Instruments. 1: Beam Splitters". Applied Optics. 10 (11):

Directed graph (1,937 words) [view diff] exact match in snippet view article find links to article

matrix, and is unique up to permutation of rows and columns. Another matrix representation for a directed graph is its incidence matrix. See direction for

Character theory (3,521 words) [view diff] exact match in snippet view article find links to article

class functions. Given a matrix representation ρ of H, Frobenius later gave an explicit way to construct a matrix representation of G, known as the representation

Dihedral group of order 8 (1,014 words) [view diff] no match in snippet view article find links to article

In mathematics, D4 (sometimes alternatively denoted by D8) is the dihedral group of degree 4 and order 8. It is the symmetry group of a square. As an example

Dot product representation of a graph (277 words) [view diff] exact match in snippet view article find links to article

Electronic Journal of Combinatorics, 18 (1): Paper 216, doi:10.37236/703, MR 2853073. Media related to Matrix representation of graphs at Wikimedia Commons

Conjugate transpose (1,735 words) [view diff] case mismatch in snippet view article find links to article

Canonical Matrices," 1932. Chasnov, Jeffrey R. (4 February 2022). "1.6: Matrix Representation of Complex Numbers". Applied Linear Algebra and Differential Equations

Quantum Fourier transform (3,302 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \omega ^{8}=\left(e^{\frac {i2\pi }{8}}\right)^{8}=1} . The matrix representation of the Fourier transform on three qubits is: F 8 = 1 8 [ 1 1 1 1

Hiptmair–Xu preconditioner (1,662 words) [view diff] exact match in snippet view article find links to article

H_{h}(\operatorname {curl} )} space, A v g r a d {\displaystyle A_{vgrad}} is the matrix representation of discrete vector Laplacian defined on [ H h ( grad ) ] n {\displaystyle

Toeplitz operator (547 words) [view diff] exact match in snippet view article find links to article

operator on H 2 {\displaystyle H^{2}} is Toeplitz if and only if its matrix representation, in the basis { z n , z ∈ C , n ≥ 0 } {\displaystyle \{z^{n},z\in

Schur orthogonality relations (2,618 words) [view diff] exact match in snippet view article find links to article

\Gamma ^{(\lambda )}(R)_{mn}} be a matrix element of an irreducible matrix representation Γ ( λ ) {\displaystyle \Gamma ^{(\lambda )}} of a finite group G

Random dynamical system (1,799 words) [view diff] exact match in snippet view article find links to article

S\rightarrow S} . Each such map has a n × n {\displaystyle n\times n} matrix representation, called deterministic transition matrix. It is a binary matrix but

Ingela Brimberg (342 words) [view diff] exact match in snippet view article find links to article

Herlitz, Kristina; Brimberg, Ingela (1 June 1996). "Developing the matrix representation grid (MRG): A method for observing group processes. Findings from

Exact cover (4,328 words) [view diff] exact match in snippet view article find links to article

contains the corresponding element, and is 0 otherwise. In the matrix representation, an exact cover is a selection of rows such that each column contains

Mumford–Tate group (814 words) [view diff] exact match in snippet view article find links to article

algebraic torus T used to describe Hodge structures has a concrete matrix representation, as the 2×2 invertible matrices of the shape that is given by the

Rapidity (2,057 words) [view diff] exact match in snippet view article find links to article

Since cosh (–w) = cosh w and sinh –w = – sinh w, the following matrix representation of the hyperbolic rotation will bring the moving frame into perpendicularity

Centrality (6,738 words) [view diff] exact match in snippet view article find links to article

dense adjacency matrix representation of the graph, and for edges takes Θ ( E ) {\displaystyle \Theta (E)} in a sparse matrix representation. The definition

Knuth's Algorithm X (1,335 words) [view diff] exact match in snippet view article find links to article

using dancing links in a process Knuth calls "DLX". DLX uses the matrix representation of the exact cover problem, implemented as doubly linked lists of

Metric tensor (general relativity) (2,490 words) [view diff] exact match in snippet view article

metric used in special relativity. In the above coordinates, the matrix representation of η is η = ( − c 2 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ) {\displaystyle

Dual quaternion (4,786 words) [view diff] exact match in snippet view article find links to article

related to the dual angles of the three spatial displacements. The matrix representation of the quaternion product is convenient for programming quaternion

C-symmetry (5,729 words) [view diff] exact match in snippet view article find links to article

is not representation-independent, but depends on the specific matrix representation chosen for the gamma group (the subgroup of the Clifford algebra

Schur decomposition (1,518 words) [view diff] exact match in snippet view article find links to article

clear that, with respect to this orthogonal decomposition, A has matrix representation (one can pick here any orthonormal bases Z1 and Z2 spanning Vλ and

Algebraic decision diagram (429 words) [view diff] case mismatch in snippet view article find links to article

"Multi-Terminal Binary Decision Diagrams: An Efficient Data Structure for Matrix Representation". Formal Methods in System Design. 10 (2): 149–169. doi:10.1023/A:1008647823331

Killing form (1,865 words) [view diff] exact match in snippet view article find links to article

in g {\displaystyle {\mathfrak {g}}} viewed in their fundamental matrix representation):[citation needed] The table shows that the Dynkin index for the

Diffeomorphism (4,165 words) [view diff] exact match in snippet view article find links to article

if and only if D f x {\displaystyle Df_{x}} is a bijection. The matrix representation of D f x {\displaystyle Df_{x}} is the n × n {\displaystyle n\times

Blockmodeling (1,967 words) [view diff] exact match in snippet view article find links to article

multiple links in a network, it is called a simple network.: 8 A matrix representation of a graph is composed of ordered units, in rows and columns, based

Pushforward (differential) (2,483 words) [view diff] exact match in snippet view article

{\displaystyle x} (with respect to the standard coordinates) is the matrix representation of the total derivative of φ {\displaystyle \varphi } at x {\displaystyle

Baby monster group (695 words) [view diff] exact match in snippet view article find links to article

algebra structure if it is reduced modulo 2. The smallest faithful matrix representation of the Baby Monster is of size 4370 over the finite field of order

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

a finite homomorphic image of the (2,3,7) triangle group. The matrix representation given above constitutes an embedding into Dickson's group G2(4)

Chirgwin–Coulson weights (5,667 words) [view diff] no match in snippet view article find links to article

In modern valence bond (VB) theory calculations, Chirgwin–Coulson weights (also called Mulliken weights) are the relative weights of a set of possible

Volume form (2,341 words) [view diff] exact match in snippet view article find links to article

{\displaystyle |g|} is the absolute value of the determinant of the matrix representation of the metric tensor on the manifold. The volume form is denoted

Superoperator (820 words) [view diff] exact match in snippet view article find links to article

\rangle \!\rangle } denotes a vector in the Fock-Liouville space. The matrix representation of L ( A ) {\displaystyle {\mathcal {L}}(A)} is then calculated

Projective connection (1,260 words) [view diff] exact match in snippet view article find links to article

matrices with ( w j ) = 0 {\displaystyle (w_{j})=0} . Relative to the matrix representation above, the Maurer-Cartan form of G is a system of 1-forms ( ξ ,

Ford–Fulkerson algorithm (2,299 words) [view diff] exact match in snippet view article find links to article

Graph: """ This class represents a directed graph using adjacency matrix representation. """ def __init__(self, graph): self.graph = graph # residual graph

Markov random field (2,817 words) [view diff] exact match in snippet view article find links to article

that the trace of a matrix is log of the determinant, with the matrix representation of a graph arising from the graph's incidence matrix. The importance

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

is a filter such as a muffler on an exhaust system. A transfer matrix representation of it may look like, [ P 2 Q 2 ] = [ T 11 T 12 T 21 T 22 ] [ P 1

Hamburger moment problem (1,385 words) [view diff] exact match in snippet view article find links to article

operator: T ¯ {\displaystyle {\overline {T}}} has a tridiagonal Jacobi matrix representation. This in turn leads to a tridiagonal model of positive Hankel kernels

Normal mode (3,284 words) [view diff] exact match in snippet view article find links to article

^{2}m-2k)A_{1}+kA_{2}&=0\\kA_{1}+(\omega ^{2}m-2k)A_{2}&=0\end{aligned}}} And in matrix representation: [ ω 2 m − 2 k k k ω 2 m − 2 k ] ( A 1 A 2 ) = 0 {\displaystyle

Davidon–Fletcher–Powell formula (991 words) [view diff] exact match in snippet view article find links to article

{\displaystyle B_{k}} , the DFP formula can be expressed as a compact matrix representation. Specifically, defining S k = [ s 0 s 1 … s k − 1 ] , {\displaystyle

Biquaternion (3,237 words) [view diff] exact match in snippet view article find links to article

introduce the general concepts of Lie theory. When viewed in the matrix representation, G is called the special linear group SL(2,C) in M(2, C). Many of

Neural machine translation (3,901 words) [view diff] exact match in snippet view article find links to article

process x {\displaystyle \mathbf {x} } and encode it into a vector or matrix representation of the source sentence. Then they use a decoder network that usually

Homogeneous relation (2,184 words) [view diff] exact match in snippet view article find links to article

Na Pacific Pa Philippine Ph South american SA Scotia Sc Somali So Matrix representation of the relation "is adjacent to" on the set of tectonic plates

Voigt notation (1,380 words) [view diff] case mismatch in snippet view article find links to article

Peter Helnwein (February 16, 2001). "Some Remarks on the Compressed Matrix Representation of Symmetric Second-Order and Fourth-Order Tensors". Computer Methods

Spectral theorem (3,852 words) [view diff] exact match in snippet view article find links to article

v_{2}\})^{\perp }} . Finite induction then finishes the proof. The matrix representation of A in a basis of eigenvectors is diagonal, and by the construction

Partial trace (2,121 words) [view diff] exact match in snippet view article find links to article

\ldots ,f_{n}} ⁠, be bases for V and W respectively; then T has a matrix representation { a k ℓ , i j } 1 ≤ k , i ≤ m , 1 ≤ ℓ , j ≤ n {\displaystyle \{a_{k\ell

Spacetime algebra (7,332 words) [view diff] exact match in snippet view article find links to article

the Dirac matrices over the field of real numbers;: x explicit matrix representation is unnecessary for STA. Products of the basis vectors generate a

Lam's problem (831 words) [view diff] exact match in snippet view article find links to article

or columns is exactly 1 {\displaystyle 1} . Using the incidence matrix representation, Lam's problem is equivalent to determining if there is a way of

Input–output model (4,053 words) [view diff] exact match in snippet view article find links to article

of two interlinked departments. Leontief was the first to use a matrix representation of a national (or regional) economy. The model depicts inter-industry

Symmetric rank-one (1,155 words) [view diff] exact match in snippet view article find links to article

{\displaystyle m\ll n} ). The limited-memory matrix is based on a compact matrix representation B k = B 0 + J k N k − 1 J k T , J k = Y k − B 0 S k , N k = D k

List of terms relating to algorithms and data structures (3,135 words) [view diff] exact match in snippet view article find links to article

address-calculation sort adjacency list representation adjacency matrix representation adversary algorithm algorithm BSTW algorithm FGK algorithmic efficiency

Sequence graph (698 words) [view diff] exact match in snippet view article find links to article

other structural rearrangements that wouldn't be allowable in a matrix representation. If there are multiple possible paths when traversing a thread in

Timeline of thermodynamics (3,324 words) [view diff] exact match in snippet view article find links to article

Fermi–Dirac statistics 1927 – John von Neumann introduces the density matrix representation, establishing quantum statistical mechanics 1928 – John B. Johnson

Trace (linear algebra) (5,564 words) [view diff] exact match in snippet view article

can define the trace of this map by considering the trace of a matrix representation of f, that is, choosing a basis for V and describing f as a matrix

Laguerre transformations (3,431 words) [view diff] exact match in snippet view article find links to article

represented as a 2×2 matrix whose entries are dual numbers. The matrix representation of z ↦ p z + q r z + s {\displaystyle z\mapsto {\frac {pz+q}{rz+s}}}

Chromosome (evolutionary algorithm) (2,686 words) [view diff] exact match in snippet view article

representing a permutation, for example the ordinal representation or the matrix representation. When a genetic representation contains, in addition to the decision

Quaternion group (3,716 words) [view diff] exact match in snippet view article find links to article

convention for the SU ⁡ ( 2 ) {\displaystyle \operatorname {SU} (2)} matrix representation to make contact with the usual Pauli matrices: e ↦ ( 1 0 0 1 ) =

Francis Y. L. Chin (720 words) [view diff] case mismatch in snippet view article find links to article

Security Henry Leung and Francis Chin, "Finding Exact Optimal Motif in Matrix Representation by Partitioning", Proceedings of the 4th European Conference on

Vibronic coupling (2,761 words) [view diff] exact match in snippet view article find links to article

PMID 15267642. Chernyak, Vladimir; Mukamel, Shaul (2000). "Density-matrix representation of nonadiabatic couplings in time-dependent density functional (TDDFT)

Conway group Co1 (756 words) [view diff] exact match in snippet view article find links to article

Co1 is on the 98280 pairs {v,–v} of norm 4 vectors. There is a matrix representation of dimension 24 over the field F 2 {\displaystyle \mathbb {F} _{2}}

Fibonacci sequence (13,066 words) [view diff] exact match in snippet view article find links to article

convergents of any continued fraction has a determinant of +1 or −1. The matrix representation gives the following closed-form expression for the Fibonacci numbers:

Casimir element (3,663 words) [view diff] exact match in snippet view article find links to article

representations). For a given value of ℓ {\displaystyle \ell } , the matrix representation is ( 2 ℓ + 1 ) {\displaystyle (2\ell +1)} -dimensional. Thus, for

Cayley–Dickson construction (2,554 words) [view diff] exact match in snippet view article find links to article

p(qr). For the reason of this non-associativity, octonions have no matrix representation. The algebra immediately following the octonions is called the sedenions

Pythagorean quadruple (1,383 words) [view diff] exact match in snippet view article find links to article

parametrized by (m, n, p, q) corresponds to the first column of the matrix representation E(α) of conjugation α(⋅)α by the Hurwitz quaternion α = m + ni +

Higman–Sims group (1,525 words) [view diff] exact match in snippet view article find links to article

100 |M22|, and there are instances of HS including a permutation matrix representation of the Mathieu group M22. If an instance of HS in Co0 fixes a particular

Quantum harmonic oscillator (6,952 words) [view diff] exact match in snippet view article find links to article

where U j i {\displaystyle U_{ji}} is an element in the defining matrix representation of U(N). The energy levels of the system are E = ℏ ω [ ( n 1 + ⋯

Fractional matching (1,424 words) [view diff] exact match in snippet view article find links to article

|X| = |Y| = n, and M is a perfect fractional matching, then the matrix representation of M is a doubly stochastic matrix - the sum of elements in each

Representation theory (7,269 words) [view diff] exact match in snippet view article find links to article

choose a basis for V to identify V with Fn, and hence recover a matrix representation with entries in the field F. An effective or faithful representation

Peter Balazs (mathematician) (643 words) [view diff] case mismatch in snippet view article

(7/8): 623–637. Retrieved 25 November 2022. Balazs, Peter (2008). "Matrix Representation of Operators Using Frames". Sampling Theory in Signal and Image

Matrix (mathematics) (13,681 words) [view diff] exact match in snippet view article

group SU(3); for their calculations, physicists use a convenient matrix representation known as the Gell-Mann matrices, which are also used for the SU(3)

Avoided crossing (2,614 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \textstyle {\begin{pmatrix}0\\1\end{pmatrix}}} as the matrix representation of eigenstates | ψ 1 ⟩ {\displaystyle \textstyle |\psi _{1}\rangle

Cauchy–Riemann equations (5,011 words) [view diff] exact match in snippet view article find links to article

v/\partial x=-\partial u/\partial y} . A matrix of this form is the matrix representation of a complex number. Geometrically, such a matrix is always the

Nonlinear eigenproblem (1,767 words) [view diff] exact match in snippet view article find links to article

as well as nonlinear eigenvalue problems, designed from density-matrix representation in quantum mechanics combined with contour integration techniques

Alexander Varchenko (2,033 words) [view diff] exact match in snippet view article find links to article

representation of the KZ equations was identified with the associated R-matrix representation. This construction gave a geometric proof of the Kohno-Drinfeld

Generalizations of Pauli matrices (2,766 words) [view diff] exact match in snippet view article find links to article

X_{1}Z_{2}=X\otimes Z\otimes I.} The traditional Pauli matrices are the matrix representation of the s u ( 2 ) {\displaystyle {\mathfrak {su}}(2)} Lie algebra

Task allocation and partitioning in social insects (3,836 words) [view diff] exact match in snippet view article find links to article

But they also argue that the input to the function should be a matrix representation (of time spent by each individual on each task), in order to provide

Multiple sequence alignment (6,213 words) [view diff] exact match in snippet view article find links to article

penalty. The alignment of individual motifs is then achieved with a matrix representation similar to a dot-matrix plot in a pairwise alignment. An alternative

Counterfactual thinking (4,854 words) [view diff] exact match in snippet view article find links to article

to counterfactual reasoning through two phases. The first uses a matrix representation of logical operations inspired by neural models of distributed memories

Direct linear transformation (2,152 words) [view diff] exact match in snippet view article find links to article

where [ x k ] × {\displaystyle [\mathbf {x} _{k}]_{\times }} is the matrix representation of the vector cross product. Notice that this last equation is vector

Extensions of symmetric operators (3,248 words) [view diff] exact match in snippet view article find links to article

C_{A}(A+1)x=(A-1)x.\quad {\mbox{i.e.}}\quad C_{A}=(A-1)(A+1)^{-1}.\,} which have matrix representation[clarification needed] C A = [ Γ 1 Γ 3 D Γ 1 ] : ran ⁡ ( A + 1 )

Quantum logic gate (10,339 words) [view diff] exact match in snippet view article find links to article

More generally if U is a gate that operates on a single qubit with matrix representation U = [ u 00 u 01 u 10 u 11 ] , {\displaystyle

Conway group Co2 (1,028 words) [view diff] exact match in snippet view article find links to article

copies of -η also fixes the same vector. Hence Co2 has a convenient matrix representation inside the standard representation of Co0. The trace of ζ is -8

Formal concept analysis (5,372 words) [view diff] exact match in snippet view article find links to article

each entry ki,j equals to 1 if "object i has attribute j." In this matrix representation, each formal concept corresponds to a maximal submatrix (not necessarily

Calculus of moving surfaces (1,501 words) [view diff] exact match in snippet view article find links to article

temporal symbols ( B β α {\displaystyle B_{\beta }^{\alpha }} is a matrix representation of the surface's curvature shape operator) The ∇ ˙ {\displaystyle

Bloch's theorem (6,060 words) [view diff] exact match in snippet view article find links to article

groups are one dimensional. Given they are one dimensional the matrix representation and the character are the same. The character is the representation

Landscape connectivity (3,511 words) [view diff] exact match in snippet view article find links to article

population j {\displaystyle j} . Many ecological models rely on this matrix representation. For instance, the matrix product M i j n {\displaystyle \mathbf

Stokes parameters (4,348 words) [view diff] exact match in snippet view article find links to article

.22..351M. doi:10.1119/1.1933744. William H. McMaster (1961). "Matrix representation of polarization". Rev. Mod. Phys. 33 (1): 8. Bibcode:1961RvMP..

Eisenbud–Levine–Khimshiashvili signature formula (1,722 words) [view diff] exact match in snippet view article find links to article

fractions. Applying this to the multiplication table gives the matrix representation of the bilinear form β with respect to the given basis: [ 0 0 0

Minkowski space (10,458 words) [view diff] exact match in snippet view article find links to article

tangent to cotangent spaces, explicitly given by the inverse of η in matrix representation, can be used to define raising of an index. The components of this

Molecular dynamics (10,208 words) [view diff] exact match in snippet view article find links to article

function of this sum. Semi-empirical potentials make use of the matrix representation from quantum mechanics. However, the values of the matrix elements

Quantum walk (2,600 words) [view diff] exact match in snippet view article find links to article

which, with respect to the standard z-component spin basis, has matrix representation H = 1 2 ( 1 1 1 − 1 ) {\displaystyle H={\frac {1}{\sqrt

Impedance analogy (2,745 words) [view diff] exact match in snippet view article find links to article

the electrical equivalent circuit and vice versa. The impedance matrix representation of a transducer transforms force in the mechanical domain into current

Dual system (12,271 words) [view diff] exact match in snippet view article find links to article

F:\mathbb {K} ^{n}\to \mathbb {K} ^{n}} is a linear operator, and the matrix representation of F {\displaystyle F} with respect to E {\displaystyle {\mathcal

Matroid (8,774 words) [view diff] exact match in snippet view article find links to article

matroids under another name, but there are often reasons to favor the matrix representation. A matroid that is equivalent to a vector matroid, although it may

Group testing (9,934 words) [view diff] exact match in snippet view article find links to article

later studied more fully by Katona in 1973. Katona introduced the matrix representation of non-adaptive group-testing and produced a procedure for finding

Square root of a matrix (4,651 words) [view diff] exact match in snippet view article find links to article

i\ } and hence all complex numbers using 2×2 real matrices, see matrix representation of complex numbers. Just as with the real numbers, a real matrix

Sum-of-squares optimization (2,695 words) [view diff] exact match in snippet view article find links to article

x ) {\textstyle p(x)} and a i ( x ) {\textstyle a_{i}(x)} in a matrix representation. This program is generally non-convex, because the constraints (1)

Rational motion (1,805 words) [view diff] exact match in snippet view article find links to article

} where [ H 2 n ( t ) ] {\displaystyle [H^{2n}(t)]} is the matrix representation of the rational Bézier motion of degree 2 n {\displaystyle 2n} in

Mathematical descriptions of the electromagnetic field (6,726 words) [view diff] exact match in snippet view article find links to article

have the same algebraic properties of the gamma matrices but their matrix representation is not needed. The derivative is now ∇ = γ μ ∂ μ . {\displaystyle

Representation of a Lie group (5,246 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \operatorname {GL} (n;\mathbb {C} )} . This is known as a matrix representation. Two representations of G on vector spaces V, W are equivalent if

Neural coding (8,112 words) [view diff] exact match in snippet view article find links to article

learning, a representation learning method which aims to find a sparse matrix representation of the input data in the form of a linear combination of basic elements

Abstract polytope (4,552 words) [view diff] exact match in snippet view article find links to article

abstract polytope may be shown as: In this accumulated incidence matrix representation the diagonal entries represent the total counts of either element

Multispecies coalescent process (5,675 words) [view diff] exact match in snippet view article find links to article

like the majority rule extended ("greedy") consensus method or the matrix representation with parsimony (MRP) supertree approach, will not be consistent

Ghost leg (1,705 words) [view diff] exact match in snippet view article find links to article

ghost leg, then Mn = I for some finite n. For any ghost leg with matrix representation M, there exists a ghost leg with representation M−1, such that M

Context-dependent memory (7,757 words) [view diff] exact match in snippet view article find links to article

Other attributes of a memory make up the remainder of the memory matrix representation of a particular memory item, in an array model for association.

Derivations of the Lorentz transformations (11,515 words) [view diff] exact match in snippet view article find links to article

equivalent way of saying this is that h {\displaystyle h} has the matrix representation ( − I n 0 0 I p ) {\displaystyle {\begin{pmatrix}-I_{n}&0\\0&I_{p}\end{pmatrix}}}

One-way quantum computer (6,454 words) [view diff] exact match in snippet view article find links to article

applying a (Controlled) C Z {\displaystyle CZ} gate operation. The matrix representation of such two-qubits operator is given by C Z = [ 1 0 0 0 0 1 0 0

Affine focal set (2,066 words) [view diff] exact match in snippet view article find links to article

(X,Y)\mapsto d_{Y}(d_{X}\Delta )} . This is the two-form whose matrix representation is the Hessian matrix. It has already been seen that h ( X , Z )

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

a column vector (x, y)T, then multiplication from the left by a matrix representation of a quaternion produces a new column vector representing the correct

Geometric algebra (13,801 words) [view diff] exact match in snippet view article find links to article

{\displaystyle k\mapsto -e_{1}e_{2}} ⁠. Every associative algebra has a matrix representation; replacing the three Cartesian basis vectors by the Pauli matrices

Affine symmetric group (10,247 words) [view diff] exact match in snippet view article find links to article

entries satisfy certain inequalities. Their procedure uses the matrix representation of affine permutations and generalizes the shadow construction,

Weyl algebra (4,164 words) [view diff] exact match in snippet view article find links to article

on the left by ∂ x j {\displaystyle \partial _{x_{j}}} . In the matrix representation, similar to the matrix mechanics, A 1 {\displaystyle A_{1}} is represented

Causal fermion systems (5,050 words) [view diff] exact match in snippet view article find links to article

orthonormal basis ( ψ i ) {\displaystyle (\psi _{i})} have the matrix representation ( F ( x ) ) j i = − ψ i ( x ) ¯ ψ j ( x ) {\displaystyle {\big (}F(x){\big

Wigner D-matrix (4,717 words) [view diff] exact match in snippet view article find links to article

)\otimes \mathbf {D} ^{j'}(\alpha ,\beta ,\gamma )} forms a reducible matrix representation of the groups SO(3) and SU(2). Reduction into irreducible components

Density matrix renormalization group (3,481 words) [view diff] exact match in snippet view article find links to article

Form the ( d ∗ 3 ) × ( d ∗ 3 ) {\displaystyle (d*3)\times (d*3)} matrix representation of operators for the system composite of the block and left-site

Classical XY model (4,861 words) [view diff] exact match in snippet view article find links to article

_{n}^{*}(\theta ')\psi _{n}(\theta )} which represents a diagonal matrix representation in the basis of its plane-wave eigenfunctions ψ = exp ⁡ ( i n θ

Nervous system network models (5,049 words) [view diff] exact match in snippet view article find links to article

relationships. Another representation of the connectivity is by matrix representation (See Sporns, O. (2007)). Hilgetag, C. C. (2002) describes the computational

Cayley–Hamilton theorem (11,251 words) [view diff] exact match in snippet view article find links to article

Therefore it is not surprising that the theorem holds. There is no such matrix representation for the octonions, since the multiplication operation is not associative

Linear belief function (3,955 words) [view diff] exact match in snippet view article find links to article

representing the six special cases, we see a clear advantage of the moment matrix representation, i.e., it allows a unified representation for seemingly diverse

Rotation formalisms in three dimensions (9,999 words) [view diff] exact match in snippet view article find links to article

parametrization due to the following properties: More compact than the matrix representation and less susceptible to round-off errors The quaternion elements

Proofs involving ordinary least squares (5,246 words) [view diff] exact match in snippet view article find links to article

parameter values. The normal equations can be derived directly from a matrix representation of the problem as follows. The objective is to minimize S ( β )

Eigenstate thermalization hypothesis (5,544 words) [view diff] exact match in snippet view article find links to article

Conversely if a quantum many-body system satisfies the ETH, the matrix representation of any local operator in the energy eigen basis is expected to follow

Krippendorff's alpha (5,534 words) [view diff] exact match in snippet view article find links to article

expressed in terms of the visually more instructive coincidence matrix representation of the reliability data. A coincidence matrix cross tabulates the

Majorana equation (8,807 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \,C\,} is a 4×4 matrix, the charge conjugation matrix. The matrix representation of C {\displaystyle \,C\,} depends on the choice of the representation

Glossary of engineering: M–Z (31,177 words) [view diff] exact match in snippet view article find links to article

powerful controlling principle underlying quantum transitions. A matrix representation of P (in any number of dimensions) has determinant equal to −1,

Chemical graph generator (5,049 words) [view diff] exact match in snippet view article find links to article

overlaps among substructures. Once the structure is built in the matrix representation, the saturated molecule is stored in the output list. The COCOA

Klaus Halbach (963 words) [view diff] exact match in snippet view article find links to article

1230H. doi:10.1103/PhysRev.119.1230. Halbach, K. (February 1964). "Matrix representation of Gaussian optics" (PDF). American Journal of Physics. 32 (2):

Tensor (machine learning) (4,104 words) [view diff] exact match in snippet view article

Narendra, Ahuja (2005), Rank-R approximation of tensors using image-as-matrix representation, IEEE Computer Society Conference on Computer Vision and Pattern

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

space. Mathematically, it the Givens rotation has the following matrix representation: G ( i , j , ϕ ) = [ 1 ⋯ 0 ⋯ 0 ⋯ 0 ⋮ ⋱ ⋮ ⋮ ⋮ 0 ⋯ cos ⁡ ( ϕ ) ⋯ sin