Abstract
It is well known that the square matrix, of rank n−k + 1,which we shall denote by B where any element to the left of, or below the nonzero diagonal b1, k, b2, k + 1, . …, bn−k + 1, n is zero, can be resolved into factors Z−1DZ; where D is a square matrix of order n having the elements d1, k, d2, k + 1, . …, dn−k + 1, n all unity and all the other elements zero, and where Z is a non-singular matrix. In this paper we shall show in a particular case that this is so, and in the case in question we shall exhibit the matrix Z explicitly. Application of this is made to find the classical canonical form of a rational integral function of a square matrix A.
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