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arXiv · 2510.25631

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

Sweta Das·Andrii Dmytryshyn·Volker Mehrmann
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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.

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Sweta Das, Andrii Dmytryshyn, Volker Mehrmann. 2025-10-29. Canonical forms for pairs of matrices associated with Lagrangian and Dirac subspaces. https://arxiv.org/abs/2510.25631

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