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Enumerating
diagonalizable matrices over $\mathbb{Z}_{p^k}$
Catherine Falvey, Heewon Hah, William Sheppard, Brian Sittinger and Rico Vicente
Vol. 13 (2020), No. 2, 323–344
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Abstract |
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Although a good portion of elementary linear algebra concerns itself with matrices over a field such as or , many combinatorial problems naturally surface when we instead work with matrices over a finite field. As some recent work has been done in these areas, we turn our attention to the problem of enumerating the square matrices with entries in that are diagonalizable over . This turns out to be significantly more nontrivial than its finite-field counterpart due to the presence of zero divisors in . |
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Keywords
eigenvalues, matrices, finite commutative rings
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Mathematical Subject Classification 2010
Primary: 05A05, 05C22, 15A18, 15B33
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Milestones
Received: 12 August 2019
Revised: 27 November 2019
Accepted: 23 December 2019
Published: 30 March 2020
Communicated by Stephan Garcia
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Authors |
| Catherine Falvey | |
| American University Washington, D.C. United States |
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| Heewon Hah | |
| University of North Carolina Charlotte, NC United States |
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| William Sheppard | |
| University of California Santa Barbara, CA United States |
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| Brian Sittinger | |
| California State University Channel
Islands Camarillo, CA United States |
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| Rico Vicente | |
| California State University Long Beach, CA United States |
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