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2020 Enumerating diagonalizable matrices over $\mathbb{Z}_{p^k}$
Catherine Falvey, Heewon Hah, William Sheppard, Brian Sittinger, Rico Vicente
Involve 13(2): 323-344 (2020). DOI: 10.2140/involve.2020.13.323

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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Catherine Falvey. Heewon Hah. William Sheppard. Brian Sittinger. Rico Vicente. "Enumerating diagonalizable matrices over $\mathbb{Z}_{p^k}$." Involve 13 (2) 323 - 344, 2020. https://doi.org/10.2140/involve.2020.13.323

Information

Received: 12 August 2019; Revised: 27 November 2019; Accepted: 23 December 2019; Published: 2020
First available in Project Euclid: 25 June 2020

zbMATH: 07184487
MathSciNet: MR4080497
Digital Object Identifier: 10.2140/involve.2020.13.323

Subjects:
Primary: 05A05, 05C22, 15A18‎, 15B33

Rights: Copyright © 2020 Mathematical Sciences Publishers

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