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Bezoutians of rational matrix functions, matrix equations and factorizations

✍ Scribed by Leonid Lerer; Leiba Rodman

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
210 KB
Volume
302-303
Category
Article
ISSN
0024-3795

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✦ Synopsis

The notion of Bezoutian for a quadruple of rational matrix functions introduced by the authors in previous works is shown to be an adequate connecting link between certain factorization problems for rational matrix functions and quadratic and linear matrix equations. Particular attention is given to various types of coprime factorizations. A characterization of Bezoutians as angle operators between certain pairs of subspaces is also given.

πŸ“œ SIMILAR VOLUMES

Bezoutians of Rational Matrix Functions
Bezoutians of Rational Matrix Functions
✍ Leonid Lerer; Leiba Rodman πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 870 KB

Various concepts of a Bezoutian of two rational matrix functions are introduced, thereby extending this concept (previously studied in the framework of matrix and operator polynomials and analystic functions) beyond the class of analytic functions. Basic properties of the Bezoutians are established.

Existence of minimal nonsquare J-symmetr
Existence of minimal nonsquare J-symmetric factorizations for self-adjoint rational matrix functions
✍ L Lerer; M.A Petersen; A.C.M Ran πŸ“‚ Article πŸ“… 2004 πŸ› Elsevier Science 🌐 English βš– 244 KB

In this paper we show that any rational matrix function having hermitian values on the imaginary axis, and with constant signature and constant pole signature admits a minimal symmetric factorization with possibly nonsquare factors. Our proof is based on a construction which shows that any such func