Ela Matrix Functions Preserving Sets

Ela Matrix Functions Preserving Sets of Generalized Nonnegative Matrices

Matrix functions preserving several sets of generalized nonnegative matrices are characterized. These sets include PFn, the set of n×n real eventually positive matrices; and WPFn, the set of matrices A ∈ R such that A and its transpose have the Perron-Frobenius property. Necessary conditions and sufficient conditions for a matrix function to preserve the set of n× n real eventually nonnegative ...

Linear preserving gd-majorization functions from Mn,m to Mn,k

Linear Functions Preserving Sut-Majorization on RN

Suppose $textbf{M}_{n}$ is the vector space of all $n$-by-$n$ real matrices, and let $mathbb{R}^{n}$ be the set of all $n$-by-$1$ real vectors. A matrix $Rin textbf{M}_{n}$ is said to be $textit{row substochastic}$ if it has nonnegative entries and each row sum is at most $1$. For $x$, $y in mathbb{R}^{n}$, it is said that $x$ is $textit{sut-majorized}$ by $y$ (denoted by $ xprec_{sut} y$) if t...

Ela Norm Estimates for Functions of Two Commuting

Matrix valued analytic functions of two commuting matrices are considered. A precise norm estimate is established. As a particular case, the matrix valued functions of two matrices on tensor products of Euclidean spaces are explored.

Ela the Szegö Matrix Recurrence and Its Associated Linear Non-autonomous Area-preserving Map

A change to the Szegö matrix recurrence relation, satisfied by orthonormal polynomials on the unit circle, gives rise to a linear map by the action of matrices belonging to the group SU(1; 1). The companion factorization of such matrices, via 2-order linear homogeneous difference equations, provides a compact representation of the orthogonal polynomial on the circle. Moreover, an isomorphism SU...