We derive an algorithm based on the boundedness of these second derivatives for the global minimization of an eigenvalue of an analytic Hermitian matrix function. The algorithm is globally convergent. It determines the globally minimal value of a piece-wise quadratic under-estimator for the eigen...
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 ...
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...
摘要: Asymptotic growth rates are obtained for the eigenvalues of a partitioned Hermitian matrix having positive definite and negative definite complementary principal submatrices, when the nonprincipal submatrix grows indefinitely large. (Author)关键词:...
摘要: We first investigate the Hermitian matrices with k distinct eigenvalues,and then give an algebraic characterization to a graph with k distinct eigenvalues with respect to the adjacency and(normalized) Laplacian matrix.关键词: Hermitian matrix positive semidefinite matrix adjacency matrix Laplacian ...
In this note we show how to compute the spectrum of G by computing the spectrum of two smaller graphs, namely a (modified) form of the covered graph H and another graph which we term the anti-cover. This is done for both the adjacency matrix and the normalized Laplacian. We also give...
Let R is an element of C-nxn be a nontrivial involution, i.e., R-2 = I and R not equal +/- I. A is an element of C-nxn is called anti-Hermitian R-symmetric... GX Huang,F Yin - APPLIED MATHEMATICS AND COMPUTATION -ELSEVIER- 被引量: 0发表: 2007年 Mirror-Symmetric matrices...
Some matrix... Bengt,Lindberg - 《Journal of Chemical Physics》 被引量: 104发表: 1988年 Analytical eigenstates for the quantum Rabi model We develop a method to find analytical solutions for the eigenstates of the quantum Rabi model. These include symmetric, anti-symmetric and asymmetric anal....
is the order of matrixAused in the computation. Specified as: an integer;n0. kd Ifuplo='U',kdis the number of superdiagonals of the matrixA. Ifuplo='L',kdis the number of subdiagonals. Specified as: an integer;kd0. ab the real symmetric or ...
Concavity of certain matrix trace and norm functions We refine Epstein's method to prove joint concavity/convexity of matrix trace functions of Lieb typeTrf(Φ(Ap)1/2Ψ(Bq)Φ(Ap)1/2)and symmetric (anti-) norm... Hiai,Fumio - 《Linear Algebra & Its Applications》 被引量: 25发表: 2016...