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Minimal Pencil Realizations of Rational Matrix Functions with Symmetries

Published online by Cambridge University Press:  20 November 2018

Ilya Krupnik  and
Peter Lancaster
Ilya Krupnik
Affiliation:
Department of Mathematics and Statistics University of Calgary Calgary, Alberta T2N 1N4
Peter Lancaster
Affiliation:
Department of Mathematics and Statistics University of Calgary Calgary, Alberta T2N 1N4
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Abstract

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A theory of minimal realizations of rational matrix functions $W(\lambda )$ in the “pencil” form $W(\lambda )=C{{(\lambda {{A}_{1}}-{{A}_{2}})}^{-1}}B$ is developed. In particular, properties of the pencil $\text{ }\!\!\lambda\!\!\text{ }{{A}_{1}}\,-\,{{A}_{2}}$ are discussed when $W(\lambda )$ is hermitian on the real line, and when $W(\lambda )$ is hermitian on the unit circle.

Keywords

93Bxx15A23
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 41 , Issue 2 , 01 June 1998 , pp. 178 - 186
Copyright
Copyright © Canadian Mathematical Society 1998

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