Proportion of cyclic matrices in maximal reducible matrix algebras

JOURNAL OF ALGEBRA

卷:369

Article

Brown, Scott²  Giudici, Michael²  Glasby, S. P.^1,3  Praeger, Cheryl E.^2,4 

[1] Cent Washington Univ, Dept Math, Ellensburg, WA 98926 USA

[2] Univ Western Australia, Sch Math & Stat, Ctr Math Symmetry & Computat, Nedlands, WA 6009, Australia

[3] Univ Canberra, Fac Informat Sci & Engn, Canberra, ACT 2601, Australia

[4] King Abdulaziz Univ, Jeddah 21413, Saudi Arabia

关键词: Cyclic matrix;    Density;    Reducible matrix algebra;    MEAT-AXE;    Upper and lower bounds;    Cyclic module;   

DOI  :  10.1016/j.jalgebra.2012.06.024

来源: Elsevier

【 摘 要 】

Let M(V) = M(n, F-q) denote the algebra of n x n matrices over F-q, and let M(V)(U) denote the (maximal reducible) subalgebra that normalizes a given r-dimensional subspace U of V = F-q(n) where 0 < r < n. We prove that the density of non-cyclic matrices in M(V)(U) is at least q(-2)(1 + c(1)q(-1)), and at most q(-2)(1 + c(2)q(-1)), where c(1) and c(2) are constants independent of n, r, and q. The constants c(1) = -4/3 and c(2) = 35/3 suffice. (c) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free