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Polynomial equations for matrices over finite fields

Published online by Cambridge University Press:  17 April 2009

Jiuzhao Hua
Jiuzhao Hua
Affiliation:
School of Mathematics, University of New South Wales, Sydney NSW 2052, Australia e-mail: hua@maths.unsw.edu.au
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Abstract

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Let E(x) be a monic polynomial over the finite field q of q elements. A formula for the number of n × n matrices θ over q, satisfying E(θ) = 0 is obtained by counting the representations of the algebra q[x]/(E(x)) of degree n. This simplifies a formula of Hodges.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 59 , Issue 1 , February 1999 , pp. 59 - 64
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Hodges, J. H., ‘The matrix equations X 2 − I = 0 over a finite field’, Amer. Math. Monthly 65 (1958), 518–520.CrossRefGoogle Scholar
[2]Hodges, J.H., ‘Scalar polynomial equations for matrices over a finite field’, Duke Math. J. 25 (1958), 291–296.CrossRefGoogle Scholar
[3]Macdonald, I. G., Symmetric functions and Hall polynomials (Clarendon Press, Oxford, 1979).Google Scholar