On the similarity of dual operators
type: Item
instance of: scholarly article
title: On the similarity of dual operators
zbMATH Open document ID: 1142.11022
author: Alexandru Tupan
published in: Linear Algebra and its Applications
publication date: 2008-06-09T00:00:00Z
review text: Let \(k\) be a field with an involution \(\sigma\in\Aut(k)\) and let \(\langle\;,\;\rangle: V\times W\rightarrow k\) be a non-degenerate sesquilinear form, where \(V\) and \(W\) a linear spaces over \(k\) of the same finite dimension. Let \(\Lambda\in\operatorname{End}(V)\) and \(\Lambda^*\in \operatorname{End}(W)\) be dual operators. The aim of the paper is to prove the following result: If \(\Lambda\) and \(\Lambda^*\) are similar operators, then there exists a Hermitian operator \(\varphi:V\rightarrow W\) such that \(\Lambda^*=\varphi\Lambda\varphi^{-1}.\) This result was proved by \textit{D. Z. Djokovič} [Linear Algebra Appl. 6, 155--158 (1973; Zbl 0251.15013)], but that proof was incomplete.
reviewed by: Andrzej Sładek
Mathematics Subject Classification ID: 11E39
Mathematics Subject Classification ID: 15A04
zbMATH DE Number: 5285776
zbMATH Keywords: dual operator
zbMATH Keywords: Hermitian operator
zbMATH Keywords: sesquilinear form
MaRDI profile type: Publication
full work available at URL: j.laa.2008.02.027
OpenAlex ID: W1996651712
cites work: On the similarity between a linear transformation and its adjoint
cites work: A note on the similarity of a matrix and its conjugate transpose
cites work: Matrix Analysis
cites work: On the similarity transformation between a matrix and its transpose
DOI: 10.1016/J.LAA.2008.02.027
description: scientific article; zbMATH DE number 5285776