Vol. 13, No. 2, 2020

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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
Abstract

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 pk that are diagonalizable over pk. This turns out to be significantly more nontrivial than its finite-field counterpart due to the presence of zero divisors in pk.

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Keywords
eigenvalues, matrices, finite commutative rings
Mathematical Subject Classification 2010
Primary: 05A05, 05C22, 15A18, 15B33
Milestones
Received: 12 August 2019
Revised: 27 November 2019
Accepted: 23 December 2019
Published: 30 March 2020

Communicated by Stephan Garcia
Authors
Catherine Falvey
American University
Washington, D.C.
United States
Heewon Hah
University of North Carolina
Charlotte, NC
United States
William Sheppard
University of California
Santa Barbara, CA
United States
Brian Sittinger
California State University Channel Islands
Camarillo, CA
United States
Rico Vicente
California State University
Long Beach, CA
United States