Further results on primitive factorizations for nD polynomial matrices

This paper presents some further results on primitive factorizations for nD polynomial matrices. A new necessary and sufficient condition is derived for the existence of primitive factorization for an nD polynomial matrix whose content has only simple zeros. This condition is based on testing the common zeros of the reduced minors of some matrices associated with the given matrix, and hence provides a new insight into the primitive factorization problem. The new condition is also easy to implement computationally. A nontrivial example is illustrated. It is then shown via examples that it is still difficult to determine whether or not an nD polynomial matrix admits a primitive factorization when its content has a multiple zero