The spectral spread of Hermitian matrices

Congruence of Hermitian Matrices by Hermitian Matrices

Two Hermitian matrices A, B ∈ Mn(C) are said to be Hermitian-congruent if there exists a nonsingular Hermitian matrix C ∈ Mn(C) such that B = CAC. In this paper, we give necessary and sufficient conditions for two nonsingular simultaneously unitarily diagonalizable Hermitian matrices A and B to be Hermitian-congruent. Moreover, when A and B are Hermitian-congruent, we describe the possible iner...

J-spectral factorization of regular para-Hermitian transfer matrices

-spectral factorization of regular para-Hermitian transfer matrices

This paper characterizes a class of regular para-Hermitian transfer matrices and then reveals the elementary characteristics of J -spectral factorization for this class. A transfer matrix in this class admits a J -spectral factorization if and only if there exists a common nonsingular matrix to similarly transform the A-matrices of and −1, resp., into 2 × 2 lower (upper, resp.) triangular block...

Spectral Radii of Large Non-Hermitian Random Matrices

By using the independence structure of points following a determinantal point process, we study the radii of the spherical ensemble, the truncation of the circular unitary ensemble and the product ensemble with parameter n and k. The limiting distributions of the three radii are obtained. They are not the Tracy-Widom distribution. In particular, for the product ensemble, we show that the limiti...

Perturbations of Hermitian Matrices and Applications to Spectral Symbols

It is often observed in practice that matrix sequences {An}n generated by discretization methods applied to linear differential equations, possess a Spectral Symbol, that is a measurable function describing the asymptotic distribution of the eigenvalues of An. Sequences composed by Hermitian matrices own real spectral symbols, that can be derived through the axioms of Generalized Locally Toepli...