Proportion of cyclic matrices in maximal reducible matrix algebras

Authors

Scott Brown, University of Western Australia
Michael Giudici, University of Western Australia
Stephen P. Glasby, Central Washington University
Cheryl E. Praeger, University of Western Australia

Document Type

Article

Department or Administrative Unit

Mathematics

Publication Date

11-1-2012

Abstract

Let M(V)=M(n,F_q) denote the algebra of n×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=Fⁿ_q where 0U is at least q⁻²(1+_c1q⁻¹),and at most q⁻²(1+_c2q⁻¹),where _c1 and _c2 are constants independent of n, r, and q. The constants c1=−4/3 and c2=35/3 suffice.

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

Brown, S., Giudici, M., Glasby, S. P., & Praeger, C. E. (2012). Proportion of cyclic matrices in maximal reducible matrix algebras. Journal of Algebra, 369, 360–368. https://doi.org/10.1016/j.jalgebra.2012.06.024

Journal

Journal of Algebra

Copyright

Copyright © 2012 Elsevier Inc. All rights reserved.