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

@article{Elsheikh2014RelatingE,
title={Relating \$p\$-Adic eigenvalues and the local Smith normal form},
author={Mustafa Elsheikh and Mark Giesbrecht},
journal={ArXiv},
year={2014},
volume={abs/1401.1773}
}

Determinantal ideals of graphs generalize, among others, the spectrum and the Smith normal form (SNF) of integer matrices associated to graphs. In this work we investigate the relationship of the… Expand

The ultimate goal is to extend the applications of numerical algorithms for computing eigenvalues to computing the invariant factors of symbolic matrices as well as to design an algorithm for computing uniform samples from the nullspace.Expand

Determinantal ideals of graphs generalize, among others, the spectrum and the Smith normal form (SNF) of integer matrices associated to graphs. In this work we investigate the relationship of the… Expand

P-adic numbers p-adic interpolation of the reimann zeta-function p-adic power series rationality of the zeta-function of a set of equations over a finite field (Part contents).

We present a new algorithm to compute the Integer Smith normal form of large sparse matrices. We reduce the computation of the Smith form to independent, and therefore parallel, computations modulo… Expand

For matrices A and b with entries of bounded size and dimensions n x n and n x 1, this method can be implemented in time O(n3(logn) 2) which is better than methods previously used.Expand

Douglas Wiedemann’s (1986) landmark approach to solving sparse linear systems over finite fields provides the symbolic counterpart to non-combinatorial numerical methods for solving sparse linear… Expand

An algorithm which is time- and memory-efficient when the number of nontrivial invariant factors is small is given, and a method for dimension reduction while preserving the invariant Factors is described.Expand