Abstract
In this chapter results of the previous chapter are specified further for rational matrix functions of a special type, namely for the so-called companion based functions. These are characterized by the fact that they are rational matrix function having a minimal realization in which both the main matrix and the associate main matrix are (first) companions. A description of such functions is presented for the 2 × 2 case, and necessary and sufficient conditions are given for such functions to admit a complete factorization. The factorization results in this chapter are based on a detailed analysis of simultaneous reduction to complementary forms of pairs of companion matrices.
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© 2008 Birkhäuser Verlag AG
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(2008). Complete Factorization of Companion Based Matrix Functions. In: Factorization of Matrix and Operator Functions: The State Space Method. Operator Theory: Advances and Applications, vol 178. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8268-1_12
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DOI: https://doi.org/10.1007/978-3-7643-8268-1_12
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8267-4
Online ISBN: 978-3-7643-8268-1
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