Anti-diagonals of symmetric and skew symmetric matrices with prescribed eigenvalues
type: Item
instance of: scholarly article
title: Anti-diagonals of symmetric and skew symmetric matrices with prescribed eigenvalues
zbMATH Open document ID: 1269.15010
author: Wen Yan
author: Tin-Yau Tam
published in: Linear Algebra and its Applications
publication date: 2013-01-16T00:00:00Z
review text: This paper deals with symmetric and skew symmetric matrices with prescribed eigenvalues. The authors obtain a complete relationship between the \(k\)-th anti-diagonals and the eigenvalues of an \(n\times n\) real symmetric matrix. They also characterize the anti-diagonals of real and complex skew symmetric matrices in terms of their eigenvalues.
reviewed by: Edgar Pereira
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15A29
zbMATH DE Number: 6125877
zbMATH Keywords: symmetric matrix
zbMATH Keywords: skew symmetric matrix
zbMATH Keywords: \(k\)-th anti-diagonal
zbMATH Keywords: prescribed eigenvalues
MaRDI profile type: Publication
full work available at URL: j.laa.2012.08.038
OpenAlex ID: W2073420020
cites work: Short proofs of theorems of Mirsky and Horn on diagonals and eigenvalues of matrices
cites work: Diagonal elements and eigenvalues of a real symmetric matrix
cites work: Doubly Stochastic Matrices and the Diagonal of a Rotation Matrix
cites work: Antidiagonals of matrices in a unitary similarity orbit
cites work: Inequalities: theory of majorization and its applications
cites work: Kostant's convexity theorem and the compact classical groups
cites work: A Lie Theoretic Approach to Thompson's Theorems on Singular Values-Diagonal Elements and Some Related Results
cites work: Singular Values, Diagonal Elements, and Convexity
cites work: A note on constructing a symmetric matrix with specified diagonal entries and eigenvalues
DOI: 10.1016/J.LAA.2012.08.038
description: scientific article; zbMATH DE number 6125877