A note on Potter's theorem for quasi-commutative matrices
type: Item
instance of: scholarly article
title: A note on Potter's theorem for quasi-commutative matrices
zbMATH Open document ID: 1177.15019
author: Raphael Loewy
author: Volker Mehrmann
published in: Linear Algebra and its Applications
publication date: 2009-03-17T00:00:00Z
review text: The authors discuss the converse of a theorem of \textit{H. S. A. Potter} [Am. Math. Mon. 57, 321--322 (1950; Zbl 0040.00501)] stating that if a matrix equation \(AB=\omega BA\) is satisfied with \(\omega\) a primitive \(q\)th root of unity, then \(A^q+B^q=(A+B)^q\). They modify both conditions in order to get a converse and they present a characterization when the converse holds for these modified conditions and \(q=3\), and a conjecture for the general case.
reviewed by: Andreas Arvanitoyeorgos
Mathematics Subject Classification ID: 15A27
Mathematics Subject Classification ID: 15A24
zbMATH DE Number: 5529488
zbMATH Keywords: quasi-commutative matrices
zbMATH Keywords: roots of unity
zbMATH Keywords: Potter's theorem
zbMATH Keywords: matrix equation
MaRDI profile type: Publication
full work available at URL: j.laa.2008.08.005
OpenAlex ID: W2053585832
cites work: Q3254327
cites work: Potter, Wielandt, and Drazin on the Matrix Equation AB = wBA: New Answers to Old Questions
cites work: On the Latent Roots of Quasi-Commutative Matrices
DOI: 10.1016/J.LAA.2008.08.005
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description: scientific article; zbMATH DE number 5529488