Relating $p$-adic eigenvalues and the local Smith normal form

Abstract

Conditions are established under which the $p$-adic valuations of the invariant factors (diagonal entries of the Smith form) of an integer matrix are equal to the $p$-adic valuations of the eigenvalues. It is then shown that this correspondence is the typical case for "most" matrices; precise density bounds are given for when the property holds, as well as easy transformations to this typical case.

To appear in Linear Algebra and Its Applications

Cited by in corpus (1)

• Eigenvalues, Smith normal form and determinantal ideals