Linear preservers on triangular matrices
type: Item
instance of: scholarly article
title: Linear preservers on triangular matrices
zbMATH Open document ID: 0886.15004
DOI: 10.1016/S0024-3795(97)00069-4
published in: Linear Algebra and its Applications
publication date: 1998-05-04T00:00:00Z
review text: Let \(T_n(F)\) be the vector space of all \(n\times n\) upper triangular matrices over a field \(F\). Rank one preservers \(T\) on \(T_n(F)\) are characterized if they satisfy one of the following properties: (1) \(T\) preserves rank one matrices, (2) \(T\) preserves both singular and nonsingular matrices, (3) \(T\) is nonsingular and \(T(\text{adj } A)=\text{adj } T(A)\) for all \(A\in T_n(F)\). The determinant preserving linear transformations on \(T_n(F)\) is also characterized. Nonsingular linear transformations which commute with the adjugate function by using the structure of rank one preservers on \(T_n(F)\) are discussed.
Mathematics Subject Classification ID: 15A04
Mathematics Subject Classification ID: 15A03
zbMATH DE Number: 1100773
zbMATH Keywords: linear preservers
zbMATH Keywords: rank one preservers
zbMATH Keywords: triangular matrices
zbMATH Keywords: linear transformations
author: Wai-Leong Chooi
author: Ming-Huat Lim
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1100773