The number of Kronecker indices of square pencils of a special kind
type: Item
instance of: scholarly article
title: The number of Kronecker indices of square pencils of a special kind
zbMATH Open document ID: 0953.15017
DOI: 10.1016/S0024-3795(99)00207-4
author: E. Marques de Sá
author: Yulin Zhang
published in: Linear Algebra and its Applications
publication date: 2001-01-31T00:00:00Z
review text: Let \({\mathcal A},{\mathcal B}\) be similarity classes of \(n\times n\) matrices over a field \(F\). The authors prove that the ranks of the matrix pencils \(xA+B\) \((A\in {\mathcal A},B\in {\mathcal B})\) form the closed interval with end points \(\max\{r_{\mathcal A},r_{\mathcal B}\}\) and \(\min\{r_{\mathcal A}+r_{\mathcal B},n\}\) where \(r_{\mathcal A},r_{\mathcal B}\) are the ranks of the members of \({\mathcal A},{\mathcal B}\). Since the number of Kronecker indices of \(xA+B\) is its nullity \(n-\text{rank}(xA+B)\), this result is of some significance for the classification of the pencils in question.
reviewed by: G. E. Wall
Mathematics Subject Classification ID: 15A22
Mathematics Subject Classification ID: 15A03
zbMATH DE Number: 1419710
zbMATH Keywords: similarity classes
zbMATH Keywords: ranks
zbMATH Keywords: matrix pencils
zbMATH Keywords: Kronecker indices
zbMATH Keywords: classification
MaRDI profile type: Publication
cites work: Q3261425
cites work: Ranks of submatrices and the off-diagonal indices of a square matrix
cites work: The eigenvalues of the product of matrices with prescribed similarity classes*
cites work: The rank of the difference of matrices with prescribed similarity classes
cites work: Spectrally complete pairs of matrices
cites work: On the number of invariant polynomials of the product of matrices with prescribed similarity classes
full work available at URL: s0024-3795(99)00207-4
OpenAlex ID: W1973169526
description: scientific article; zbMATH DE number 1419710