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

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. [ABSTRACT FROM AUTHOR]