Bounds on the coefficients of the characteristic and minimal polynomials

Jean-Guillaume Dumas (1)

1 CASYS - Calculs Algébriques et Systèmes Dynamiques

This note presents absolute bounds on the size of the coefficients of the characteristic and minimal polynomials depending on the size of the coefficients of the associated matrix. Moreover, we present algorithms to compute more precise input-dependant bounds on these coefficients. Such bounds are e.g. useful to perform deterministic chinese remaindering of the characteristic or minimal polynomial of an integer matrix.

Mots clés: characteristic polynomial coefficient bound

Domaines: Calcul formel [cs.SC]

Jean-Guillaume Dumas. Bounds on the coefficients of the characteristic and minimal polynomials. Journal of Inequalities in Pure and Applied Mathematics, 2007, 8 (2), art. 31, 6pp. ⟨hal-00086820v7⟩