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.

中文翻译：

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实 H-自伴矩阵的翻转正交共轭对称 Jordan 规范基的存在性

对于不定内积中的自伴实矩阵，有两种特殊的规范若尔当形式，即 (i) 翻转正交 (FO) 和 (ii) γ -共轭对称 (CS)。这些是经典的 Jordan 形式，由于它们是H-自伴这一事实而具有某些附加属性。在本文中，我们证明对于任何实数H -自伴矩阵，存在同时翻转正交和 γ -共轭对称的γ -FOCS Jordan 形式。