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

✍ Scribed by ALLAN STEEL

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 476 KB
Volume: 24
Category: Article
ISSN: 0747-7171
DOI: 10.1006/jsco.1996.0142

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✦ Synopsis

A new algorithm is presented for the computation of canonical forms of matrices over fields. These are the Primary Rational, Rational, and Jordan canonical forms. The algorithm works by obtaining a decomposition of the vector space acted on by the given matrix into primary cyclic 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.

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