Canonical forms for pairs of matrices associated with Lagrangian and Dirac subspaces

Sweta Das; Andrii Dmytryshyn; Volker Mehrmann

Canonical forms for pairs of matrices associated with Lagrangian and Dirac subspaces

Representation Theory 2025-10-30 v1 Rings and Algebras

Authors: Sweta Das , Andrii Dmytryshyn , Volker Mehrmann

Abstract

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.

Keywords

canonical forms matrix pairs Lagrangian subspaces Dirac subspaces Hamiltonian systems

Cite

@article{arxiv.2510.25631,
  title  = {Canonical forms for pairs of matrices associated with Lagrangian and Dirac subspaces},
  author = {Sweta Das and Andrii Dmytryshyn and Volker Mehrmann},
  journal= {arXiv preprint arXiv:2510.25631},
  year   = {2025}
}

Canonical forms for pairs of matrices associated with Lagrangian and Dirac subspaces

Abstract

Keywords

Cite

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