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Generalisation of the Perron-Frobenius theory to matrix pencils

Please always quote using this URN:urn:nbn:de:0296-matheon-3741
  • We present a new extension of the well-known Perron-Frobenius theorem to regular matrix pairs $(E,A)$. The new extension is based on projector chains and is motivated from the solution of positive differential-algebraic systems or descriptor systems. We present several examples where the new condition holds, whereas conditions in previous literature are not satisfied.

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Metadaten
Author:Volker Mehrmann, Reinhard Nabben, Elena Virnik
URN:urn:nbn:de:0296-matheon-3741
Referee:Peter Deuflhard
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2007/01/24
Release Date:2007/01/24
Tag:
Institute:Technische Universität Berlin
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 / 15A22 Matrix pencils [See also 47A56]
Preprint Number:369
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