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Erschienen in:
2008 | OriginalPaper | Buchkapitel
Factorization into Degree One Factors
Erschienen in: Factorization of Matrix and Operator Functions: The State Space Method
Verlag: Birkhäuser Basel
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In this chapter we study the factorization of a proper rational
m × m
matrix function having the value
I
m
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.