The MEAT-AXE and f-cyclic matrices

JOURNAL OF ALGEBRA

卷:300

Article

Glasby, S. P.

关键词: MEAT-AXE;    f-cyclic;    irreducible;    reducible;    algorithm;   

DOI  :  10.1016/j.jalgebra.2006.01.026

来源: Elsevier

【 摘 要 】

Let M(d, F) denote the algebra of d x d matrices over a field F, and denote by m(X)(t) and c(X)(t) the minimal and the characteristic polynomials of X is an element of M(d, F). We call X an f-cyclic matrix if f is an irreducible factor of mX(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 of f-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. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free