Hong's canonical form of a Hermitian matrix with respect to orthogonal *congruence
type: Item
instance of: scholarly article
title: Hong's canonical form of a Hermitian matrix with respect to orthogonal *congruence
zbMATH Open document ID: 1477.15034
author: Tadej Starčič
published in: Linear Algebra and its Applications
publication date: 2021-09-29T00:00:00Z
review text: Two matrices \(M\) and \(N\) are orthogonally *congruent if \(S^*MS = N\) for some orthogonal matrix \(S = (S^T)^{-1}\). The main result of this paper is: Theorem. Each Hermitian matrix is orthogonally *congruent to exactly one matrix of the form (1.5) (see the paper), determined up to a permutation of direct summands. The proof uses the fact that two matrices \(M\) and \(N\) are orthogonally *congruent precisely when there exists an orthogonal solution \(X\) of the equation \(M\bar{X} = NX\). The proof is long but easy to follow thanks to two auxiliary lemmas.
reviewed by: Rosário Fernandes
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 15A23
Mathematics Subject Classification ID: 15B10
zbMATH DE Number: 7403449
zbMATH Keywords: canonical form
zbMATH Keywords: complex orthogonal matrix
zbMATH Keywords: Hermitian matrix
zbMATH Keywords: symmetric matrix
zbMATH Keywords: simultaneous reduction
MaRDI profile type: Publication
full work available at URL: j.laa.2021.08.007
OpenAlex ID: W3195407956
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DOI: 10.1016/J.LAA.2021.08.007
description: scientific article; zbMATH DE number 7403449