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Symmetric factorizations and localization of zeroes of rational matrix functions. (English) Zbl 0866.15003

Summary: Symmetric factorizations of selfadjoint rational matrix functions are studied using the concept of Bezoutian for rational matrix functions as the main tool. In particular, the distribution of zeroes of a rational matrix function \(F(\lambda)\) is described in terms of inertia of the Bezoutian corresponding to symmetric factorizations of \(\Gamma(\lambda)=(F(\overline\lambda))^*F(\lambda)\). Symmetric factorizations \(\Gamma(\lambda)=(G(\overline\lambda))^*G(\lambda)\) are constructed so that \(F(\lambda)\) and \(G(\lambda)\) are coprime in a certain sense.

MSC:

15A23 Factorization of matrices
15A54 Matrices over function rings in one or more variables
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