Kilic. Numerical optimization of eigenvalues of Hermitian matrix functions. SIAM J. Matrix Anal. Appl., 35(2):699-724, 2014.E. Mengi, E.A. Yildirim, and M. Kilic. Numerical optimization of eigenvalues of Hermi- tian matrix functions. SIAM J. Matrix Anal. Appl., 2013. Submitted....
The eigenvalues of an indentity matrix Enter key to drop response here. The eigenvalues of an orthogonal matrix Enter key to drop response here. The eigenvalues of a Hermitian matrix Enter key to drop response here. The eigenvalues of a triangular matrix ...
Hermitian matrices have real eigenvalues. The Cauchy interlace theorem states that the eigenvalues of a Hermitian matrix A of order n are interlaced with those of any principal submatrix of order n 1. Theorem 1 (Cauchy Interlace Theorem). Let A be a Hermitian matrix of order n, and let B ...
Degeneracy of the eigenvalues of hermitian matrices is analyzed in terms of algebraic relations between the matrix elements. Only finite-dimensional matrices are considered, representing Hamiltonians of spin systems in particular.The analysis is in terms of linear relations in the space of 'diagonal' ...
We prove this in two sentences using only the linearity of the determinant, and the fact that all eigenvalues of a symmetric matrix are real.doi:10.48550/arXiv.math/0502408Fisk, SteveMathematicsS. Fisk. A very short proof of Cauchy's interlace theorem for eigenvalues of Hermitian matrices, ar...
All the eigenvalues of a Hermitian matrix are realRemember that a matrix is said to be Hermitian if and only if it equals its conjugate transpose: Hermitian matrices have the following nice property. Proposition Let be a matrix. If is Hermitian, then all its eigenvalues are real (i.e., ...
Hermitian matrixrank-one modificationSUMMARYIn this paper, we present some new interlacing properties about the bounds of the eigenvalues for rank-one modification of Hermitian matrix, whose eigenvalues are different and spectral decomposition also needs to be known. Numerical examples demonstrate the ...
Let a=(a19, an) and β=(β19, βn) be arbitrary nonincreasing sequences of real numbers. We consider the question: for which nonincreasing sequences 7=(yl9, 7) do there exist Hermitian matrices A and B such that A, B and A+ B have a, β and 7 respectively as their DOI: 10...
In this paper, we study the trace and the eigenvalues of a positive definite Hermitian matrix and get inequalities about the trace and eigenvalues between the Schur complement of the sum of positive definite Hermiteian matrix and the sum of the Schur complements of positive definite Hermiteian mat...
In addition, numerical problems will arise if the Hermitian matrix (or a particular submatrix of ...