Structure-preserving Diagonalization of Matrices in Indefinite Inner Product Spaces
| Autor: | Philip Saltenberger |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Algebra and Number Theory 15B57 15B10 15A23 15A63 11E39 Skew Structure (category theory) Numerical Analysis (math.NA) 010103 numerical & computational mathematics Unitary matrix 01 natural sciences Unitary state Matrix (mathematics) Inner product space FOS: Mathematics Mathematics - Numerical Analysis 0101 mathematics Symplectic geometry Mathematics |
| Zdroj: | The Electronic Journal of Linear Algebra. 36:21-37 |
| ISSN: | 1081-3810 |
| DOI: | 10.13001/ela.2020.5071 |
| Popis: | In this work some results on the structure-preserving diagonalization of selfadjoint and skewadjoint matrices in indefinite inner product spaces are presented. In particular, necessary and sufficient conditions on the symplectic diagonalizability of (skew)-Hamiltonian matrices and the perplectic diagonalizability of per(skew)-Hermitian matrices are provided. Assuming the structured matrix at hand is additionally normal, it is shown that any symplectic or perplectic diagonalization can always be constructed to be unitary. As a consequence of this fact, the existence of a unitary, structure-preserving diagonalization is equivalent to the existence of a specially structured additive decomposition of such matrices. The implications of this decomposition are illustrated by several examples. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|