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.
Author: | Leonhard Batzke, Christian Mehl |
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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 |