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DC Field | Value | Language |
---|---|---|
dc.contributor.author | Loewy, Raphael | |
dc.contributor.author | Mehrmann, Volker | |
dc.date.accessioned | 2021-12-17T10:08:08Z | - |
dc.date.available | 2021-12-17T10:08:08Z | - |
dc.date.issued | 2008-02-11 | |
dc.identifier.issn | 2197-8085 | |
dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/15651 | - |
dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-14424 | - |
dc.description.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. | en |
dc.language.iso | en | en |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
dc.subject.ddc | 510 Mathematik | en |
dc.subject.other | quasi-commutative matrices | en |
dc.subject.other | roots of unity | en |
dc.subject.other | Potter's theorem | en |
dc.title | A note on Potter's theorem for quasi-commutative matrices | en |
dc.type | Research Paper | en |
tub.accessrights.dnb | free | en |
tub.publisher.universityorinstitution | Technische Universität Berlin | en |
tub.series.issuenumber | 2008, 04 | en |
tub.series.name | Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin | en |
dc.type.version | submittedVersion | en |
tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik | de |
tub.subject.msc2000 | 15A27 Commutativity | en |
Appears in Collections: | Technische Universität Berlin » Publications |
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