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On the inverse eigenvalue problem for $T$-alternating and $T$-palindromic matrix polynomials

Please always quote using this URN:urn:nbn:de:0296-matheon-12513
  • The inverse eigenvalue problem for $T$-alternating matrix polynomials over arbitrary algebraically closed fields of characteristic different from two is considered. The main result shows that the necessary conditions obtained in \cite{MacMMM10} for a matrix polynomial to be the Smith form of a $T$-alternating matrix polynomial are under mild conditions also sufficient to be the Smith form of a $T$-alternating matrix polynomial with invertible leading coefficient which is additionally in anti-triangular form.. In particular, this result implies that any $T$-alternating matrix polynomial with invertible leading coefficient is equivalent to a $T$-alternating matrix polynomial in anti-triangular form that has the same finite and infinite elementary divisors as the original matrix polynomial. Finally, the inverse eigenvalue problem for $T$-palindromic matrix polynomials is considered excluding the case that both $+1$ and $-1$ are eigenvalues.

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Metadaten
Author:Leonhard Batzke, Christian Mehl
URN:urn:nbn:de:0296-matheon-12513
Referee:Volker Mehrmann
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2013/10/08
Release Date:2013/10/08
Tag:alternating matrix polynomial; matrix polynomial; palindromic matrix polynomial; triangularization
Institute:Technische Universität Berlin
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F15 Eigenvalues, eigenvectors
Preprint Number:1035
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