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Splitting fields for characteristic polynomials of matrices with entries in a finite field
Journal article   Peer reviewed

Splitting fields for characteristic polynomials of matrices with entries in a finite field

Eric Schmutz
Finite fields and their applications, v 14(1), pp 250-257
2008

Abstract

Characteristic polynomial Finite field Random matrix Splitting field
Let M n be the set of all n × n matrices with entries in the finite field F q . Let X ( A ) be the degree of the splitting field of the characteristic polynomial of A, and let μ n be the average degree: μ n = 1 | M n | ∑ A ∈ M n X ( A ) . A theorem of Reiner is used to prove that, as n → ∞ , μ n = e B n / log n ( 1 + o ( 1 ) ) , where B is an explicit constant.

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Web of Science research areas
Mathematics
Mathematics, Applied
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