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Journal Articles Journal of Inequalities in Pure and Applied Mathematics Year : 2007

Bounds on the coefficients of the characteristic and minimal polynomials

Abstract

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.
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Dates and versions

hal-00086820 , version 1 (19-07-2006)
hal-00086820 , version 2 (20-07-2006)
hal-00086820 , version 3 (21-07-2006)
hal-00086820 , version 4 (24-10-2006)
hal-00086820 , version 5 (26-01-2007)
hal-00086820 , version 6 (05-02-2007)
hal-00086820 , version 7 (21-09-2007)

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Cite

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⟩
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