Canonical forms for pairs of matrices associated with Lagrangian and Dirac subspaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917049419169792 |
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| author | Das, Sweta Dmytryshyn, Andrii Mehrmann, Volker |
| author_facet | Das, Sweta Dmytryshyn, Andrii Mehrmann, Volker |
| contents | We derive the canonical forms for a pair of $n\times n$ complex matrices $(E,Q)$ under transformations $(E,Q) \rightarrow (UEV,U^{-T}QV)$, and $(E,Q) \rightarrow (UEV,U^{-*}QV)$, where $U$ and $V$ are nonsingular complex matrices. We, in particular, consider the special cases of $E^TQ$ and $E^*Q$ being (skew-)symmetric and (skew-)Hermitian, respectively, that are associated with Lagrangian and Dirac subspaces and related linear-time invariant dissipative Hamiltonian descriptor systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_25631 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Canonical forms for pairs of matrices associated with Lagrangian and Dirac subspaces Das, Sweta Dmytryshyn, Andrii Mehrmann, Volker Representation Theory Rings and Algebras 15A21, 15A22, 15A24 We derive the canonical forms for a pair of $n\times n$ complex matrices $(E,Q)$ under transformations $(E,Q) \rightarrow (UEV,U^{-T}QV)$, and $(E,Q) \rightarrow (UEV,U^{-*}QV)$, where $U$ and $V$ are nonsingular complex matrices. We, in particular, consider the special cases of $E^TQ$ and $E^*Q$ being (skew-)symmetric and (skew-)Hermitian, respectively, that are associated with Lagrangian and Dirac subspaces and related linear-time invariant dissipative Hamiltonian descriptor systems. |
| title | Canonical forms for pairs of matrices associated with Lagrangian and Dirac subspaces |
| topic | Representation Theory Rings and Algebras 15A21, 15A22, 15A24 |
| url | https://arxiv.org/abs/2510.25631 |