Structure theory of reciprocal pairs of linear transformations
type: Item
instance of: scholarly article
title: Structure theory of reciprocal pairs of linear transformations
zbMATH Open document ID: 0807.15001
DOI: 10.1016/0024-3795(94)90002-7
author: Andrew Lenard
published in: Linear Algebra and its Applications
publication date: 1994-09-26T00:00:00Z
review text: If \(A\), \(B\) is a nonsingular reciprocical pair of linear transformations (i.e. acting between two vector spaces \(V\) and \(W\) in opposite directions), then the Jordan canonical forms of \(BA\) and \(AB\) are the same. This Jordan form \(J\) serves to classify completely the nonsingular pairs. Moreover, bases exist in the vector spaces \(V\) and \(W\) such that with respect to these bases both \(A\) and \(B\) appear as the matrix \(J^{1/2}\). Further one studies the cases of nilpotent reciprocical pairs. An illustrative application is also given.
Mathematics Subject Classification ID: 15A04
Mathematics Subject Classification ID: 15A21
zbMATH DE Number: 644677
zbMATH Keywords: nonsingular reciprocical pair
zbMATH Keywords: linear transformations
zbMATH Keywords: Jordan canonical forms
reviewed by: Mihail Voicu
MaRDI profile type: Publication
full work available at URL: 0024-3795(94)90002-7
OpenAlex ID: W2042340497
cites work: Elementary Divisors of AB and BA
cites work: Q4775958
cites work: REPRESENTATIONS OF QUIVERS OF INFINITE TYPE
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description: scientific article; zbMATH DE number 644677