linear algebra, eigendecomposition is the factorization of a matrix into a canonical form, whereby the matrix is represented in terms of its eigenvalues...

of matrices), and the eigenvalues of matrices (eigendecomposition of a matrix, eigenvalue perturbation theory). The set of all m × n matrices over a field...

invertible matrix (non-singular, non-degenarate or regular) is a square matrix that has an inverse. In other words, if some other matrix is multiplied...

Spectral decomposition is any of several things: Spectral decomposition for matrix: eigendecomposition of a matrix Spectral decomposition for linear operator:...

mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are...

field of graph theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix, or discrete Laplacian, is a matrix representation...

an eigendecomposition of M , {\displaystyle M,} where P {\displaystyle P} is a unitary complex matrix whose columns comprise an orthonormal basis of eigenvectors...

matrix. The eigendecomposition or diagonalization expresses A as a product VDV−1, where D is a diagonal matrix and V is a suitable invertible matrix....

An n×n matrix with n distinct nonzero eigenvalues has 2n square roots. Such a matrix, A, has an eigendecomposition VDV−1 where V is the matrix whose columns...

generalizes the eigendecomposition of a square normal matrix with an orthonormal eigenbasis to any ⁠ m × n {\displaystyle m\times n} ⁠ matrix. It is related...

mathematics, the spectrum of a matrix is the set of its eigenvalues. More generally, if T : V → V {\displaystyle T\colon V\to V} is a linear operator on any...

_{n}} of a Hermitian matrix are chosen and written as the columns of the matrix U, then one eigendecomposition of A is A = U Λ U H {\displaystyle A=U\Lambda...

decomposition M = UΣVT, U and V orthogonal, Σ diagonal matrix Eigendecomposition of a symmetric matrix (decomposition according to the spectral theorem) S...

the inverse of the matrix of eigenvectors. This is called the eigendecomposition and it is a similarity transformation. Such a matrix A is said to be...

block-encoding of A with eigendecomposition of a matrix A = ∑ λ i u i u i † {\displaystyle A=\sum \lambda _{i}u_{i}u_{i}^{\dagger }} , one can get a block-encoding...

algorithm. A tridiagonal matrix is a matrix that is both upper and lower Hessenberg matrix. In particular, a tridiagonal matrix is a direct sum of p 1-by-1...

obtaining matrix decompositions like the singular value decomposition, the QR factorization, the LU factorization, or the eigendecomposition, which can...

arbitrary matrices. Eigendecomposition of a matrix Wiener–Khinchin theorem Hawkins, Thomas (1975). "Cauchy and the spectral theory of matrices". Historia...

covariants of a matrix A can be obtained from any eigendecomposition A = SDS−1, where S is non-singular and D is diagonal with Di,i = λi. If A has no multiple...

parameter, but it also has the dual role of scale parameter. The eigendecomposition of the matrix M t {\displaystyle M^{t}} yields M i , j t = ∑ l λ l t ψ l...

to performing eigendecomposition of a matrix of connectivity weights and assigning systemic importance in proportion to the values of the principal eigenvector...

the covariance matrix. Consider the eigendecomposition of a matrix Σ g = λ g D g A g D g T , {\displaystyle \Sigma _{g}=\lambda _{g}D_{g}A_{g}D_{g}^{T}...

the Lanczos algorithm transforms the eigendecomposition problem for A {\displaystyle A} into the eigendecomposition problem for T {\displaystyle T} . For...

theorem states that the Hadamard product of two positive definite matrices is also a positive definite matrix. The result is named after Issai Schur (Schur...

amount and compute the eigendecomposition of the resulting matrix. In the case when the matrix is depicted as a near-circle, the matrix can be replaced with...

{\displaystyle A} has an eigendecomposition of the form Q E Q T {\displaystyle QEQ^{\mathrm {T} }} where E {\displaystyle E} is a diagonal matrix containing the...

solution by finding the eigendecomposition of a larger system. For the CARE, we define the Hamiltonian matrix Z = ( A − B R − 1 B ⊤ − Q − A ⊤ ) {\displaystyle...

inertia matrix is a constant real symmetric matrix. A real symmetric matrix has the eigendecomposition into the product of a rotation matrix Q {\displaystyle...

algebra, a QR decomposition, also known as a QR factorization or QU factorization, is a decomposition of a matrix A into a product A = QR of an orthonormal...

/ʃəˈlɛski/ shə-LES-kee) is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose...