It begins with a description of unitary matrices and describes them algebraically and geometrically. Special kinds of unitary matrices are given. TheQRfactorization is also discussed. Schur's theorem is presented which states that every matrix is unitarily similar to an upper triangular matrix. Then...
The symmetry of these matrices makes available techniques different from those encountered earlier in this book In particular we consider the Rayleigh quotient from which estimates for the largest and smallest eigenvalues of a symmetric or hermitian matrix can be obtained, Rayleigh's principle which is...
A uniform object-oriented solution to the eigenvalue problem for real symmetric and Hermitian matrices We present a system of classes, SHMatrix, to deal in a unified way with the computation of eigenvalues and eigenvectors in real symmetric and Hermitian mat... ME Castro,J Díaz,C Muoz-Caro,...
A Hermitian matrix is a square matrix with complex entries that is equal to its own conjugate transpose. A real matrix is Hermitian if it is symmetric. Illustration ■ A 2-by-2 Hermitian matrix A MatrixForm[A = {{3 + I, − I}, {− I, 6}}] 3+i−i−i6 The matrix A is...
Define Hermitian matrices. Hermitian matrices synonyms, Hermitian matrices pronunciation, Hermitian matrices translation, English dictionary definition of Hermitian matrices. n maths a matrix whose transpose is equal to the matrix of the complex conjugat
The entries on the main diagonal (top left to bottom right) of any Hermitian matrix are necessarily real. A matrix that has only real entries is Hermitian if and only if it is a symmetric matrix, i.e., if it is symmetric with respect to the main diagonal. A real and symmetric matrix...
Given Z, W∈ C n×m, we characterize the matrices A in S that minimize ∥ AZ W∥ (Frobenius norm), and, given an arbitrary E∈ C n×n, we find the unique matrix among the minimizers of ∥ AZ W∥ in S that minimizes ∥ A E∥. We also obtain necessary and sufficient ...
Construct a Hermitian matrix: In[1]:= Out[1]= Show the elements: Copy to clipboard. In[2]:= Direct link to example Out[3]= Scope(4) Options(1) Applications(3) Properties & Relations(4) See Also SymmetricMatrixSymmetrizedArrayHermitianMatrixQSymmetricMatrixQ ...
Hermitian-symmetric matrixCogredience transformationLCD codesHermitian LCD codesBy using the cogredience theories of an alternate matrix, a symmetric matrix and a Hermitian-symmetric matrix, we will find a special family of generator matrices for any linear code, and then using the special family ...
1) Hermitian matrix 厄尔密特矩阵 1. Using some fundamental definition and theorem of unitary space,this paper comes to several conclusions ofHermitian matrixwhich is parallel to symmetric matrix of Euclidean space. 本文利用酉空间中一些基本定义和定理,得出与欧氏空间中对称矩阵相平行的厄尔密特矩阵的几个结...