Möbius transformations of matrix polynomials
| Autor: | D. Steven Mackey, Christian Mehl, Niloufer Mackey, Volker Mehrmann |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Numerical Analysis
Polynomial Algebra and Number Theory Matrix polynomial Combinatorics Matrix (mathematics) symbols.namesake Matrix pencil symbols Discrete Mathematics and Combinatorics Canonical form Elementary divisors Geometry and Topology Invariant (mathematics) Möbius transformation Mathematics |
| Zdroj: | Linear Algebra and its Applications. 470:120-184 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2014.05.013 |
| Popis: | We discuss Mobius transformations for general matrix polynomials over arbitrary fields, analyzing their influence 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 effect 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 quadratification are investigated. We show that many important transformations are special instances of Mobius transformations, and analyze a Mobius connection between alternating and palindromic matrix polynomials. Finally, the use of Mobius transformations in solving polynomial inverse eigenproblems is illustrated. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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