✦ LIBER ✦

Strong linear preservers of symmetric doubly stochastic or doubly substochastic matrices

✍ Scribed by Shwu-Huey Lin; Bit-Shun Tam

Publisher: Elsevier Science
Year: 2004
Tongue: English
Weight: 279 KB
Volume: 379
Category: Article
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(03)00452-x

No coin nor oath required. For personal study only.

✦ Synopsis

Let S denote either the set of n × n symmetric doubly stochastic matrices or the set of n × n symmetric doubly substochastic matrices and let T be a linear map on span S. We prove that T (S) = S if and only if there exists an n × n permutation matrix P such that T (X) = P t XP for all X ∈ span S. Our proofs make use of the concept of neighborly extreme points of a polytope and depend on some intricate graph theory.

📜 SIMILAR VOLUMES

Inequalities for the spectra of symmetri

Inequalities for the spectra of symmetric doubly stochastic matrices

✍ Rajesh Pereira; Mohammad Ali Vali 📂 Article 📅 2006 🏛 Elsevier Science 🌐 English ⚖ 106 KB

A note on the boundary of the set where

A note on the boundary of the set where the decreasingly ordered spectra of symmetric doubly stochastic matrices lie

✍ Bassam Mourad 📂 Article 📅 2006 🏛 Elsevier Science 🌐 English ⚖ 172 KB

In this paper, we study the region s n of R n where the decreasingly ordered spectra of all the n×n symmetric doubly stochastic matrices lie with emphasis on the boundary set of s n . As applications, we study the case n = 4 and in particular we solve the inverse eigenvalue problem for 4×4 symmetric