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Congruence classes of matrices in GL2(Fq)

โœ Scribed by Priscilla S. Bremser

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
315 KB
Volume
118
Category
Article
ISSN
0012-365X

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โœฆ Synopsis

Given two matrices A and B in GL, ( F,), where q is a power of a prime and Fq is the finite field with q elements, we say that A and B are congruent if there is a matrix C in GL2( F,) such that A = CTBC. We show that there are q + 3 congruence classes in GL,(F,) for odd q and q + 1 classes for even q, and exhibit representatives for them.

Theorem 1. For odd q, there are q + 3 congruence class of matrices in GL2( F,).

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