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This paper is concerned with the factorization and equivalence problems ofmultivariate polynomial matrices. We present some new criteria for theexistence of matrix factorizations for a class of multivariate polynomialmatrices, and obtain a necessary and sufficient condition for the equivalenceof a square polynomial matrix and a diagonal matrix. Based on the constructiveproof of the new criteria, we give a factorization algorithm and prove theuniqueness of the factorization. We implement the algorithm on Maple, and twoillustrative examples are given to show the effectiveness of the algorithm.

New Remarks on the Factorization and Equivalence Problems for a Class of Multivariate Polynomial Matrices