Linear preservers of minimal rank
type: Item
instance of: scholarly article
title: Linear preservers of minimal rank
zbMATH Open document ID: 0968.15001
DOI: 10.1016/S0024-3795(00)00045-8
author: Leiba Rodman
author: Peter Šemrl
published in: Linear Algebra and its Applications
publication date: 2001-09-19T00:00:00Z
review text: Linear maps of upper triangular matrices preserving properties related to completion problems are studied. It is proved for a linear transformation on the vector space of upper triangular matrices that mapping the matrices of minimal rank 1 into itself and either having the analogous property with respect to matrices of full minimal rank or being bijective, is a triangular equivalence or a triangular equivalence follows after some steps. Examples including transformation of triangular similarity are added. The connection with the paper by \textit{M. Marcus} and \textit{B. N. Moyls} [Pacific J. Math. 9, 1215-1221 (1959; Zbl 0089.08902)] on rank preservers is mentioned.
Mathematics Subject Classification ID: 15A03
Mathematics Subject Classification ID: 15A29
Mathematics Subject Classification ID: 15A21
zbMATH DE Number: 1453253
zbMATH Keywords: completion problem
zbMATH Keywords: upper triangular matrices
zbMATH Keywords: minimal rank
zbMATH Keywords: triangular similarity
zbMATH Keywords: rank preservers
MaRDI profile type: Publication
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cites work: Linear Transformations on Algebras of Matrices
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cites work: Minimal rank completions for block matrices
Wikidata QID: Q127436395
description: scientific article; zbMATH DE number 1453253