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Möbius Transformations of Matrix Polynomials

Please always quote using this URN:urn:nbn:de:0296-matheon-12743
  • We discuss Möbius transformations for general matrix polynomials over arbitrary � elds, analyzing their in uence on regularity, rank, determinant, constructs such as compound matrices, and on structural features including sparsity and symmetry. Results on the preservation of spectral information contained in elementary divisors, partial multiplicity sequences, invariant pairs, and minimal indices are presented. The e� ect on canonical forms such as Smith forms and local Smith forms, on relationships of strict equivalence and spectral equivalence, and on the property of being a linearization or quadrati� cation are investigated. We show that many important transformations are special instances of Möbius transformations, and analyze a Möbius connection between alternating and palindromic matrix polynomials. Finally, the use of Möbius transformations in solving polynomial inverse eigenproblems is illustrated.

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Metadaten
Author:D. Steven Mackey, Niloufer Mackey, Christian Mehl, Volker Mehrmann
URN:urn:nbn:de:0296-matheon-12743
Referee:Jürg Kramer
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2014/02/02
Release Date:2014/02/02
Tag:Möbius transformation; matrix polynomial
Institute:Technische Universität Berlin
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F15 Eigenvalues, eigenvectors
Preprint Number:1051
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