Number of invertible/non-singular matrices over a finite field

Thread starter andreitta
Start date Nov 30, 2008
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Field Finite Matrices

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SUMMARY

The discussion focuses on determining the number of non-singular matrices (invertible matrices) of size n x n over a finite field of order q, specifically referencing the general linear group GL_n(ℱ_q). The user successfully solved the problem after considering the cardinality of GL_n(ℱ_q) and noted that the case for q = 2 can be generalized. This indicates a clear mathematical relationship between the size of the field and the structure of invertible matrices.

PREREQUISITES

Understanding of finite fields and their properties
Familiarity with linear algebra concepts, particularly matrix theory
Knowledge of the general linear group GL_n(ℱ)
Basic combinatorial counting principles

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Research the cardinality of GL_n(ℱ_q) for various values of n and q
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Mathematicians, computer scientists, and students studying linear algebra or finite fields, particularly those interested in matrix theory and its applications in areas like coding theory and cryptography.

Nov 30, 2008

andreitta

I'm trying to find the number of different non-singular matrices (nxn) over a finite field (order q). Any help would be greatly appreciated.

Thanks in advance! :)

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Nov 30, 2008

adriank

Have a look at this thread, which discusses the case where q = 2 and generalizes easily.

Nov 30, 2008

andreitta

Thanks a lot for the quick reply! I solved it already :) Hadn't thought about the cardinal of
GL_n(\mathbb{F}_q)

Thanks!

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