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Characterization and properties of matrices with generalized symmetry or skew symmetry. (English) Zbl 1046.15028
For any nontrivial involution \(R\), a complex \(n\times n\) matrix \(A\) is \(R\)-symmetric (\(R\)-skew symmetric) if \(RAR= A\) \((RAR= -A)\). The author studies many property of these notions and gives characterization of \(R\)-symmetric (resp. \(R\)-skew symmetric) matrices.

MSC:
15B57 Hermitian, skew-Hermitian, and related matrices
15A18 Eigenvalues, singular values, and eigenvectors
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