The Matrix Cauchy Index: Properties and Applications

Robert R. Bitmead, Brian D. O. Anderson

Research output: Contribution to journalArticlepeer-review

Abstract

The notion of the Cauchy index of a real rational scalar function is generalized to define 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 representations of the real rational matrix using a Laurent series, a matrix fraction description, and a state variable realization. These characteristics involve a Hankel and a Bezoutian matrix. A matrix Sturm theorem is obtained and its use for evaluating the index is indicated. Descriptions of certain impedance matrices arising in passive circuit theory are given using the matrix Cauchy index.
Original languageEnglish
Pages (from-to)655-672
JournalSIAM Journal on Applied Mathematics
Volume33
Issue number4
DOIs
Publication statusPublished - Dec 1977
Externally publishedYes

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