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) 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.
Acknowledgments
The authors are indebted to the anonymous referee for the careful reading of this manuscript, pointing out numerous typos, and giving suggestions that helped to improve the presentation of the material.
Disclosure statement
No potential conflict of interest was reported by the author(s).