On Computing the Determinant and Smith Form of an Integer Matrix

Abstract

A probabilistic algorithm is presented to find the determinant of a nonsingular, integer matrix. For a matrix A n n the algorithm requires O n3 5 logn 4 5 bit operations (assuming for now that entries in A have constant size) using standard matrix and integer arithmetic. Using asymptotically fast matrix arithmetic, a variant is described which requires O n2… (More)

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@inproceedings{Eberly2000OnCT, title={On Computing the Determinant and Smith Form of an Integer Matrix}, author={Wayne Eberly and Mark Giesbrecht and Gilles Villard}, year={2000} }