Tridiagonal canonical forms of square matrices under congruence or *congruence, pairs of symmetric or skew-symmetric matrices under congruence, and pairs of Hermitian matrices under *congruence are given over an algebraically ...

We study certain pairs of subspaces V and W of C^n we call supports that consist of eigenspaces of the eigenvalues ±‖M‖ of a minimal hermitian matrix M(‖M‖ ≤‖M+D‖ for all real diagonals D). For any pair of orthogonal ...

A system that achieves compression using artificial DNA packaging with the support of two algebraic curves is presented, whereby the Hermitian channel code algorithm introduces gain and safety. Additionally, performance ...

Given a Hermitian matrix M ∈ M3(ℂ) we describe explicitly the real diagonal matrices DM such that ║M + DM║ ≤ ║M + D║ for all real diagonal matrices D ∈ M3(ℂ), where ║ · ║ denotes the operator norm. Moreover, we generalize ...

We describe properties of a Hermitian matrix M ∈ Mn(C) having minimal quotient norm in the following sense: M M + D for all real diagonal matrices D ∈ Mn(C). Here denotes the operator norm. We show a constructive method ...

The inverse eigenvalue problem and the associated optimal approximation problem for Hermitian reflexive matrices with respect to a normal {k+1}-potent matrix are considered. First, we study the existence of the solutions ...

We present an approach to sums of random Hermitian matrices via the theory of spher- ical functions for the Gelfand pair (U(n) Herm(n), U(n)). It is inspired by a similar approach of Kieburg and Kösters for products of ...

The statistical properties of trajectories of eigenvalues of Gaussian complex matrices whose Hermitian condition is progressively broken are investigated. It is shown how the ordering on the real axis of the real eigenvalues ...