The Matrix Cauchy Index: Properties and Applicationsx
نویسنده
چکیده
Absfrset. The notion of the Cauchy indexof a real rational scalar function is generalized todefinc the Cauchy index of a real rational symmetric matrix in terms of the behavior of the matrix at real singularities of its elements. Alternative characterizations are obtained which flow from iepresenrations of the real rational matrix using a Laurent series, a matrix fraction description. and a state variable realization. These characteristics involve a Hankri and a Bezoutian matrix. A matrix Sturm theoremisobtained and its use for evaluating the indexis indicated. Descriptionsof certain impedance matrices arising in passive circuit theory are given using the matrix Cauchy index.
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