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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| 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 |
