Counting matrices over a finite field with all eigenvalues in the field
نویسندگان
چکیده
منابع مشابه
Counting Matrices Over a Finite Field With All Eigenvalues in the Field
Given a finite field F and a positive integer n, we give a procedure to count the n×n matrices with entries in F with all eigenvalues in the field. We give an exact value for any field for values of n up to 4, and prove that for fixed n, as the size of the field increases, the proportion of matrices with all eigenvalues in the field approaches 1/n!. As a corollary, we show that for large fields...
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ژورنال
عنوان ژورنال: Involve, a Journal of Mathematics
سال: 2014
ISSN: 1944-4184,1944-4176
DOI: 10.2140/involve.2014.7.627