Canonical form for H-symplectic matrices
In this paper we consider pairs of matrices (A,H), with A and H either both real or both complex, H is invertible and skew-symmetric and A is H -symplectic, that is, ATH A = H. A canonical form for such pairs is derived under the transformations (A,H) → (S −1AS, STH S) for invertible matrices S. In the canonical form for the pair, the matrix A is brought in standard (real or complex) Jordan normal form, in contrast to existing canonical forms.
KeywordsIndefinite inner product space canonical forms H -symplectic matrices
Mathematics Subject Classification (2010).Primary 15A21 15B57 15A63 Secondary 47B50
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