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Structured decompositions for matrix triples: SVD-like concepts for structured matrices

Please always quote using this URN:urn:nbn:de:0296-matheon-5210
  • Canonical forms for matrix triples $(A,G,\hat G)$, where $A$ is arbitrary rectangular and $G$, $\hat G$ are either real symmetric or skew symmetric, or complex Hermitian or skew Hermitian, are derived. These forms generalize classical product Schur forms as well as singular value decompositions. An new proof for the complex case is given, where there is no need to distinguish whether $G$ and $\hat G$ are Hermitian or skew Hermitian. This proof is independent from the results in Bolschakov/Reichstein 1995, where a similar canonical form has been obtained for the complex case, and it allows generalization to the real case. Here, the three cases, i.e., that $G$ and $\hat G$ are both symmetric, both skew symmetric or one each, are treated separately.

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Metadaten
Author:Christian Mehl, Volker Mehrmann, Hongguo Xu
URN:urn:nbn:de:0296-matheon-5210
Referee:Jürg Kramer
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2008/07/29
Release Date:2008/07/21
Tag:
Institute:Technische Universität Berlin
MSC-Classification:15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY / 15Axx Basic linear algebra / 15A21 Canonical forms, reductions, classification
65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F15 Eigenvalues, eigenvectors
65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L05 Initial value problems
65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L80 Methods for differential-algebraic equations
Preprint Number:514
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