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searching for Invertible matrix 33 found (107 total)

FEA-M (278 words) [view diff] exact match in snippet view article find links to article

pair of session keys chosen for just that message. The key is an invertible matrix used to encrypt the session keys, and the encrypted session keys must

Sylvester's law of inertia (1,431 words) [view diff] exact match in snippet view article find links to article

Namely, if A {\displaystyle A} is a symmetric matrix, then for any invertible matrix S {\displaystyle S} , the number of positive, negative and zero eigenvalues

Unisolvent functions (917 words) [view diff] exact match in snippet view article find links to article

set of functions). This is because any two bases are related by an invertible matrix (the change of basis matrix), so one basis is unisolvent if and only

Bruhat decomposition (793 words) [view diff] exact match in snippet view article find links to article

invertible matrices, so Bruhat decomposition says that one can write any invertible matrix A {\displaystyle A} as a product U 1 P U 2 {\displaystyle U_{1}PU_{2}}

Cartan's lemma (515 words) [view diff] exact match in snippet view article find links to article

matrix-valued function on a rectangle K in Cn such that F(z) is an invertible matrix for each z in K. Then there exist analytic functions F ′ {\displaystyle

Matrix mortality problem (233 words) [view diff] exact match in snippet view article find links to article

of 2 matrices, and for sets of matrices which contain at most one invertible matrix. Paterson, Michael S. (1970). "Unsolvability in 3 × 3 matrices". Studies

Sign function (2,790 words) [view diff] exact match in snippet view article find links to article

different than Q {\displaystyle {\boldsymbol {Q}}} . This leads to each invertible matrix having a unique left-signum Q {\displaystyle {\boldsymbol {Q}}} and

Greedoid (1,730 words) [view diff] exact match in snippet view article find links to article

X is an invertible matrix } . {\displaystyle F=\{X\subseteq E:{\text{ submatrix }}M_{\{1,\ldots ,|X|\},X}{\text{ is an invertible matrix}}\}.} This

Rank factorization (1,944 words) [view diff] exact match in snippet view article find links to article

{\textstyle F_{2}=R^{-1}F_{1}} gives another rank factorization for any invertible matrix R {\textstyle R} of compatible dimensions. Conversely, if A = F 1

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

{\displaystyle D(a)} can be put in upper triangular block form by the same invertible matrix P {\displaystyle P} . In other words, if there is a similarity transformation:

Cancellation property (695 words) [view diff] exact match in snippet view article find links to article

matrix equation AX = B will not have a unique solution for a non-invertible matrix A. Also note that if AB = CA and A ≠ 0 and the matrix A is invertible

Commuting matrices (1,427 words) [view diff] exact match in snippet view article find links to article

they are simultaneously diagonalizable (that is, there exists an invertible matrix P {\displaystyle P} such that both P − 1 A P {\displaystyle P^{-1}AP}

Picard–Vessiot theory (918 words) [view diff] exact match in snippet view article find links to article

a k-algebra by the coefficients of A and 1/det(A), where A is an invertible matrix over F such that B = A′/A has coefficients in F. (So A is a fundamental

Direct limit (2,071 words) [view diff] exact match in snippet view article find links to article

written as GL(K). An element of GL(K) can be thought of as an infinite invertible matrix that differs from the infinite identity matrix in only finitely many

Special linear group (1,781 words) [view diff] exact match in snippet view article find links to article

vanishing trace. The Lie bracket is given by the commutator. Any invertible matrix can be uniquely represented according to the polar decomposition as

Cartan decomposition (1,499 words) [view diff] exact match in snippet view article find links to article

the polar decomposition of a matrix. The polar decomposition of an invertible matrix is unique. Lie group decompositions Kleiner 2007 Helgason, Sigurdur

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

L n ( R ) {\displaystyle \mathrm {SL} _{n}(\mathbf {R} )} and any invertible matrix A {\displaystyle A} . Then using the two important identities det

Stability theory (2,934 words) [view diff] exact match in snippet view article find links to article

perform change-of-basis by X ′ = C X {\displaystyle X'=CX} for some invertible matrix C {\displaystyle C} , which gives X ˙ ′ = C − 1 A C X ′ {\displaystyle

Projection-slice theorem (1,224 words) [view diff] exact match in snippet view article find links to article

we consider the change of basis to be represented as B, an N-by-N invertible matrix operating on N-dimensional column vectors. Then the generalized Fourier-slice

Torsion tensor (4,375 words) [view diff] exact match in snippet view article find links to article

{\tilde {\mathbf {e} }}_{i}=\mathbf {e} _{j}{g^{j}}_{i}} for some invertible matrix-valued function (gji), then Θ ~ i = ( g − 1 ) i j Θ j . {\displaystyle

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

matrix A where A = T − 1 ∗ A T {\displaystyle A=T^{-1}*AT} for T an invertible matrix, and therefore the analysis of characteristic polynomial mentioned

Multivariate random variable (3,442 words) [view diff] exact match in snippet view article find links to article

n\times 1} column vector. If A {\displaystyle \mathbf {A} } is an invertible matrix and X {\displaystyle \textstyle \mathbf {X} } has a probability density

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

trace, meaning that tr(A) = tr(P−1AP) for any square matrix A and any invertible matrix P of the same dimensions, is a fundamental consequence. This is proved

Implicit function theorem (3,732 words) [view diff] exact match in snippet view article find links to article

implicit function theorem says that if Y {\displaystyle Y} is an invertible matrix, then there are U {\displaystyle U} , V {\displaystyle V} , and g

Regularization (mathematics) (4,623 words) [view diff] exact match in snippet view article

test set. Consider the finite approximation of Neumann series for an invertible matrix A where ‖ I − A ‖ < 1 {\displaystyle \left\|I-A\right\|<1} : ∑ i =

Nonlinear Schrödinger equation (3,272 words) [view diff] exact match in snippet view article find links to article

^{-1}\end{aligned}}} which leaves the system invariant. Here, φ is another invertible matrix solution (different from ϕ) of the Zakharov–Shabat system with spectral

Estimation of signal parameters via rotational invariance techniques (2,849 words) [view diff] exact match in snippet view article find links to article

}^{-1}} . In the sequel, it is only important that there exists such an invertible matrix F {\textstyle \mathbf {F} } and its actual content will not be important

Eigenvalue algorithm (4,870 words) [view diff] exact match in snippet view article find links to article

λi+1)vi+1 = vi and βi = 0 otherwise. More generally, if W is any invertible matrix, and λ is an eigenvalue of A with generalized eigenvector v, then

Independent component analysis (7,491 words) [view diff] exact match in snippet view article find links to article

where the A {\displaystyle A} is an m × m {\displaystyle m\times m} invertible matrix called the mixing matrix, s i {\displaystyle s_{i}} represents the

Ambisonics (6,064 words) [view diff] exact match in snippet view article find links to article

individually, and another that weights the channels through a fixed, invertible matrix to reduce redundancy. A listening-test of Opus ambisonics was published

Generalized singular value decomposition (4,126 words) [view diff] exact match in snippet view article find links to article

=0} above. Define E + = E − 1 {\displaystyle E^{+}=E^{-1}} for any invertible matrix E ∈ F n × n {\displaystyle E\in \mathbb {F} ^{n\times n}} , 0 + =

Generative adversarial network (13,881 words) [view diff] exact match in snippet view article find links to article

invertible kernel iff [ K trans ] {\displaystyle [K_{\text{trans}}]} is an invertible matrix, that is, p ≠ 1 / 4 {\displaystyle p\neq 1/4} . Continuous case: The

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

{\displaystyle y_{i}=A^{r}y_{i-1}\oplus A^{r}x_{i}.} Then, we find an invertible matrix T {\displaystyle T} and perform a change of basis, multipling the