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Derangements and eigenvalue-free elements in finite classical groups. (English) Zbl 0936.15020
One of the questions addressed in this paper is: given the matrix ring \(M(n,q)\) of \(n\times n\) matrices over the field \(F_q\) with \(q\) elements, what is the probability \(\upsilon(M;n,q)\) that a randomly chosen matrix has no eigenvalues? Regarding different \(M\), the authors derive asymptotic expressions for \(\upsilon\), in the limit \(n\to\infty\), that has as the leading term \(e^{-1}\).

MSC:
15B52 Random matrices (algebraic aspects)
20G40 Linear algebraic groups over finite fields
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