A purely algebraic method which uses the matrix Routh algor-ithm and its reverse process of the algorithm is presented to decompose a mat.ri x transfer function into a pair of right co-prime polynomial matrices or left co-pr-ime polynomial matrices. The poles and transmission zeros of the matrix transfer function arc determined from a. pair of relatively prime polynomial matrices. Also, tho common divisor of two matrix polynomials CRn be obtained by using the matrix Routh algorithm and the matrix Routh array.

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