m-NIL-CLEAN COMPANION MATRICES

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Andrada Cîmpean

Abstract

Companion matrices over fields of prime characteristic, p, that are sums of two idempotents and a nilpotent are characterized in terms of dimension and trace of such a matrix and of p. 

Companion matrices over fields of positive characteristic, p, that are sums of m idempotents, m ≥ 2, and a nilpotent are characterized in terms of dimension and trace of such a matrix and of p.

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