Abstract
This paper discusses a relationship between the prime factorizability of a normal full rank n-D ( n>2) polynomial matrix and its reduced minors. Two conjectures regarding the n-D polynomial matrix prime factorization problem are posed, and a partial solution to one of the conjectures is provided. Another related open problem of factorizing an n-D polynomial matrix that is not of normal full rank as a product of two n-D polynomial matrices of smaller size is also considered, and a partial solution to this problem is presented. An illustrative example is worked out in details.
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