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Main Title: A note on Potter's theorem for quasi-commutative matrices
Author(s): Loewy, Raphael
Mehrmann, Volker
Type: Research Paper
Abstract: We discuss the converse of a theorem of Potter stating that if the matrix equation $AB = \omega BA$ is satisfied with $\omega$ a primitive $q$th root of unity, then $A^q + B^q = (A+B)^q$. We show that both conditions have to be modified to get a converse statement and we present a characterization when the converse holds for these modified conditions and $q=3$ and a conjecture for the general case. We also present some further partial results and conjectures.
Subject(s): quasi-commutative matrices
roots of unity
Potter's theorem
Issue Date: 11-Feb-2008
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 15A27 Commutativity
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2008, 04
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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