Abstract:
Williamson's theorem on the symplectic eigenvalues of symmetric positive definite matrices is interpreted in terms of special operators of the real symplectic space and their spectra. A relation connecting the conventional and symplectic eigenvalues of a given matrix is derived.
Key words and phrases:congruence transformation, similarity transformation, symplectic matrix, Hamiltonian matrix, $J$-symmetric matrix, Schur inequality.
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