Linear operators preserving the minimal rank
type: Item
instance of: scholarly article
title: Linear operators preserving the minimal rank
zbMATH Open document ID: 0946.15019
DOI: 10.1016/S0024-3795(99)00188-3
published in: Linear Algebra and its Applications
publication date: 2000-10-12T00:00:00Z
review text: Properties of the minimal rank \(r(X)\) defined as min\(\{r(X-\lambda I):\lambda \in \mathbb{F}\}\), where \(X\) belongs to the set \(\mathbb{F}^{n \times n}\) of \(n \times n\) matrices over an algebraically closed field \(\mathbb{F}\) and \(I\) is the \(n \times n\) identity matrix, are studied. The forms of linear operators for \(n \geq 3\) and \(n = 2\) preserving the minimal rank or equivalently the number of nontrivial invariant polynomials are described. The existence of linear operators converting the minimal rank to the ordinary rank is also investigated.
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 15A03
zbMATH DE Number: 1419881
zbMATH Keywords: linear preservers
zbMATH Keywords: minimal rank
zbMATH Keywords: nontrivial invariant polynomial
author: Wasin So
MaRDI profile type: Publication
cites work: Linear transformations on matrices: The invariance of commuting pairs of matrices
cites work: Transformations on tensor product spaces
cites work: On the eigenvalues of the matrix
cites work: Linear maps that preserve commuting pairs of matrices
Wikidata QID: Q127357078
full work available at URL: s0024-3795(99)00188-3
OpenAlex ID: W2071018539
description: scientific article; zbMATH DE number 1419881