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arXiv · 2607.27218

On equivalence classes of dissipative Hamiltonian pencils

Maria Dronka
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Abstract

We study matrix pencils of the form $\lambda E - (J-R)Q$, where $Q^*E = E^*Q \geq 0$, $J^* = -J$, $R^* = R \geq 0$, and $\lambda E - Q$ is regular, in the framework of Pokrzywa's ordering of strict equivalence orbits. We characterise the maximal elements, analyse some properties of the orbit closures, and derive a restriction on possible degenerations when $Q = I$. We also consider the case where $\lambda E - Q$ may be singular, which naturally arises in the study of orbit closures, and obtain a partial result on the Kronecker canonical form. The theory is illustrated by numerous examples.

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Maria Dronka. 2026-06-25. On equivalence classes of dissipative Hamiltonian pencils. https://arxiv.org/abs/2607.27218

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