Jordan Structures of Alternating Matrix Polynomials
Please always quote using this URN:urn:nbn:de:0296-matheon-6540
- Alternating matrix polynomials, that is, polynomials whose coefficients alternate between symmetric and skew-symmetric matrices, generalize the notions of even and odd scalar polynomials. We investigate the Smith forms of alternating matrix polynomials, showing that each invariant factor is an even or odd scalar polynomial. Necessary and sufficient conditions are derived for a given Smith form to be that of an alternating matrix polynomial. These conditions allow a characterization of the possible Jordan structures of alternating matrix polynomials, and also lead to necessary and sufficient conditions for the existence of structure-preserving strong linearizations. Most of the results are applicable to singular as well as regular matrix polynomials.
Author: | D. Steven Mackey, Niloufer Mackey, Christian Mehl, Volker Mehrmann |
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URN: | urn:nbn:de:0296-matheon-6540 |
Referee: | Jürg Kramer |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2009/08/18 |
Release Date: | 2009/08/17 |
Tag: | |
MSC-Classification: | 15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY / 15Axx Basic linear algebra / 15A18 Eigenvalues, singular values, and eigenvectors |
15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY / 15Axx Basic linear algebra / 15A21 Canonical forms, reductions, classification | |
15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY / 15Axx Basic linear algebra / 15A54 Matrices over function rings in one or more variables | |
65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F15 Eigenvalues, eigenvectors | |
Preprint Number: | 660 |