Relating $p$-adic eigenvalues and the local Smith normal form
Rings and Algebras
2015-05-08 v4 Symbolic Computation
Probability
Abstract
Conditions are established under which the -adic valuations of the invariant factors (diagonal entries of the Smith form) of an integer matrix are equal to the -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.
Cite
@article{arxiv.1401.1773,
title = {Relating $p$-adic eigenvalues and the local Smith normal form},
author = {Mustafa Elsheikh and Mark Giesbrecht},
journal= {arXiv preprint arXiv:1401.1773},
year = {2015}
}
Comments
To appear in Linear Algebra and Its Applications