Article ID Journal Published Year Pages File Type
6416580 Linear Algebra and its Applications 2013 7 Pages PDF
Abstract

Let A,B be invertible n×n matrices over the finite field Fq with irreducible characteristic polynomials. For k∈Z+, denoteMk(A,B):={f(A)g(B):f,g∈Fq[x],with degf,degg4−kqmin(n,2k−1). Moreover, let d=dimKer(AB−BA), we prove|Mk(A,B)|>116(nd)(2(n−d))n−d2qk+min(k2,n−d2).

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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