The Reduced Form and Existence Theorem of the Canonical Form of Characteristic Matrices over a Skew Field

Abstract:

      Based on [1], an another kind of reduced form of characteristic matrices over a skew field is defined in this paper in a way different from that in [2], and the existence of the canonical form of a more wide class of characteristic matrices is thus established. Also, a generalization of the Cayley-Hamilton theorem to matrices over a skew field is given.