A remark on the Jordan normal form of matrices
type: Item
instance of: scholarly article
title: A remark on the Jordan normal form of matrices
zbMATH Open document ID: 0974.15003
DOI: 10.1016/S0024-3795(00)00052-5
author: Vlastimil Pták
published in: Linear Algebra and its Applications
publication date: 2001-05-15T00:00:00Z
review text: The present paper is a translation of part of an earlier one [Acta Sci. Math. Szeged 17, 190-194 (1956; Zbl 0071.24801)]. Its message is that when considering the normal form of a linear transformation \(A\) on a vector space \(X\) it pays to consider at the same time its adjoint \(A^*\) acting on the dual space. For example, it is shown in this ``geometrical'' way that there exists an \(A\)-invariant direct decomposition \(X = X_s+X_r\), where \(A\) is nilpotent on \(X_s\) and non-singular on \(X_r\).
reviewed by: G. E. Wall
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 15-03
Mathematics Subject Classification ID: 01A75
zbMATH DE Number: 1453245
zbMATH Keywords: Jordan normal form
zbMATH Keywords: reprint
zbMATH Keywords: adjoint
zbMATH Keywords: dual space
zbMATH Keywords: nilpotent
zbMATH Keywords: non-singular
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1453245