A New Algorithm for the Computation of Canonical Forms of Matrices over Fields

A new algorithm is presented for the computation of canonical forms of matrices over fields. These are thePrimaryRational,Rational, andJordancanonical forms. The algorithm works by obtaining a decomposition of the vector space acted on by the given matrix intoprimarycyclic spaces (spaces whose minimal polynomials with respect to the matrix are powers of irreducible polynomials). An efficient implementation of the algorithm is incorporated in the MAGMA Computer Algebra System.