A note on Potter’s theorem for quasi-commutative matrices |
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Authors: | Raphael Loewy Volker Mehrmann |
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Affiliation: | a Department of Mathematics, Technion, Haifa 32000, Israel b Institut für Mathematik, MA 4-5, TU Berlin, D-10623 Berlin, FRG, Germany |
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Abstract: | We discuss the converse of a theorem of Potter stating that if the matrix equation AB=ωBA is satisfied with ω a primitive qth root of unity, then Aq+Bq=(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. |
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Keywords: | 15A27 |
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