Enumerating diagonalizable matrices over ℤpk

Abstract

Although a good portion of elementary linear algebra concerns itself with matrices over a field such as ℝ or ℂ, 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 ℤpk that are diagonalizable over ℤpk. This turns out to be significantly more nontrivial than its finite-field counterpart due to the presence of zero divisors in ℤpk.