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

03/18/2022

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by   S. Dogruer Akgul, et al.

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For real matrices selfadjoint in an indefinite inner product there are two special canonical Jordan forms, that is (i) flipped orthogonal (FO) and (ii) γ-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 γ-FOCS Jordan form that is simultaneously flipped orthogonal and γ-conjugate symmetric.