The centralizer of a matrix with real quaternion elements

Abstract

Let T be a Q-endomorphism on a finite dimensional left vector space V over the division ring of real quaternions Q. In this paper we show that the centralizer of T can be regarded as an algebra over the complex numbers C and the dimension of this algebra is computed in terms of the invariant factors of T. Thus the number of C-linearly independent matrices which commute with a given matrix representing T is determined.