Abstract
Matrix equivalence over principal ideal domains is considered, using the technique of localization from commutative algebra. This device yields short new proofs for a variety of results. (Some of these results were known earlier via the theory of determinantal divisors.) A new algorithm is presented for calculation of the Smith normal form of a matrix, and examples are included. Finally, the natural analogue of the Witt–Grothendieck ring for quadratic forms is considered in the context of matrix equivalence.
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