Further Results on n-D Polynomial Matrix Factorizations

Abstract

In this paper, some new results on zero prime factorization for a normal full rank n-D (n>2) polynomial matrix are presented. Assume that d is the greatest common divisor (g.c.d.) of the maximal order minors of a given n-D polynomial matrix F1. It is shown that if there exists a submatrix F of F1, such that the reduced minors of F have no common zeros, and the g.c.d. of the maximal order minors of F equals d, then F1 admits a zero right prime (ZRP) factorization if and only if F admits a ZRP factorization. A simple ZRP factorizability of a class of n-D polynomial matrices based on reduced minors is given. An advantage is that the ZRP factorizability can be tested before carrying out the actual matrix factorization. An example is illustrated.