Title

The Meat-axe and f-cyclic matrices

Authors

Stephen P. Glasby, Central Washington University

Document Type

Article

Department or Administrative Unit

Mathematics

Publication Date

6-1-2006

Abstract

Let M(d,F) denote the algebra of d×d matrices over a field F, and denote by m_x(t) and c_x(t) the minimal and the characteristic polynomials of X ∈ M(d,F). We call X an f-cyclic matrix if f is an irreducible factor of m_x(t) which does not divide c_x(t)/m_x(t). We present a version of the MEAT-AXE algorithm that uses f-cyclic matrices. One advantage off-cyclic matrices is that they unify and generalize previous work of Parker, Holt and Rees, Ivanyos and Lux, Neumann and Praeger. The greater abundance of f-cyclic matrices may lead to an improved probability/complexity analysis of the MEAT-AXE. The difficulties that occur when the Schur index exceeds one are explored.

Comments

This article was originally published in Journal of Algebra. The full-text article from the publisher can be found here.

Due to copyright restrictions, this article is not available for free download from ScholarWorks @ CWU.

Recommended Citation

Glasby, S. P. (2006). The Meat-axe and f-cyclic matrices. Journal of Algebra, 300(1), 77–90. https://doi.org/10.1016/j.jalgebra.2006.01.026

Journal

Journal of Algebra

Copyright

Copyright © 2006 Elsevier Inc. All rights reserved.