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arXiv · 2203.09877

Existence of flipped orthogonal conjugate symmetric Jordan canonical bases for real H-selfadjoint matrices

S. Dogruer Akgul·A. Minenkova·V. Olshevsky
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Abstract

For real matrices selfadjoint in an indefinite inner product there are two special canonical Jordan forms, that is (i) flipped orthogonal (FO) and (ii) $\gamma$-conjugate symmetric (CS). These are the classical Jordan forms with certain additional properties induced by the fact that they are $H$-selfadjoint. In this paper we prove that for any real $H$-selfadjoint matrix there is a $\gamma$-FOCS Jordan form that is simultaneously flipped orthogonal and $\gamma$-conjugate symmetric.

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S. Dogruer Akgul, A. Minenkova, V. Olshevsky. 2022-03-18. Existence of flipped orthogonal conjugate symmetric Jordan canonical bases for real H-selfadjoint matrices. https://arxiv.org/abs/2203.09877

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