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arXiv · 1401.1773

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

Mustafa Elsheikh·Mark Giesbrecht
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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.

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Mustafa Elsheikh, Mark Giesbrecht. 2014-01-08. Relating $p$-adic eigenvalues and the local Smith normal form. https://doi.org/10.1016/j.laa.2015.05.001

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