Complete Factorization of Companion Based Matrix Functions

Part of the Operator Theory: Advances and Applications book series (OT, volume 178)


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.


Matrix Function Invariant Subspace Characteristic Polynomial Companion Matrix Simultaneous Reduction 
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© Birkhäuser Verlag AG 2008

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