In this chapter we study the factorization of a proper rational
m × m
matrix function having the value
at infinity into elementary factors satisfying the same constraints. These elementary factors are of McMillan degree one by definition. It turns out, by using realization, that the problem of factorizing a function in such degree one factors is intimately connected with the issue of simultaneous reduction to complementary triangular forms of pairs of matrices. We prove that factorization into elementary factors is always possible.
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