Matrix Computations—Euclidean and Non-Euclidean Domains

Abstract

So far we were essentially concerned with the inversion of matrices over fields and field of quotients constructed from the Euclidean domains (rational numbers and single variable rational functions). We now consider some of the computational problems related to matrices over the Euclidean domains (which are principal ideal rings) and general integral domains that are not Euclidean (and not principal ideal rings).