Minimal dimension of symmetric or skew-symmetric matrices of given minimal polynomial

Koulmann, P
(2001) Journal of Pure and Applied Algebra — Vol. 158, n° 2-3, p. 225-245 (2001)

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  • Koulmann, P
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Abstract
Over a field k of characteristic not 2 the set of minimal polynomials of symmetric or skew-symmetric matrices (with respect to an involution of the first kind) is known. We give the smallest possible dimension of a symmetric or skew-symmetric matrix of given minimal polynomial depending on the type of the involution. Concerning the transpose, we give the smallest constant c such that any suitable polynomial f is the minimal polynomial of a symmetric (resp. skew-symmetric) matrix of dimension c deg f. The case of polynomials of degree 2 is completely solved. (C) 2001 Elsevier Science B.V. All rights reserved.
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Koulmann, P. (2001). Minimal dimension of symmetric or skew-symmetric matrices of given minimal polynomial. Journal of Pure and Applied Algebra, 158(2-3), 225-245. https://doi.org/10.1016/S0022-4049(00)00037-2 (Original work published 2001)