Cayley-Hamilton theorem in rhotrix

Abstract

Cayley-Hamilton is one of the well-known theorems that is formulated and proved in linear algebra on matrices. In this paper we extend this theorem to the concept of rhotrix and also present some properties that are attached to it. Rhotrix is an object that lies in some way between n x n dimensional matrices and (2n -1) x (2n -1) dimensional matrices. Moreover, the representation of vectors in rhotrices is different from representation of vectors in matrices.

Keywords: Cayley-Hamilton, rhotrix, determinant, characteristic polynomial, minimum polynomial