The Meat-axe and f-cyclic matrices
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Let M(d,F) denote the algebra of d×d matrices over a field F, and denote by mx(t) and cx(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 mx(t) which does not divide cx(t)/mx(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.
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 of Algebra
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