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.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 504, 2021, pp. 61–69.
Translated by Kh. D. Ikramov.
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Ikramov, K.D., Nazari, A.M. Symplectic Eigenvalues and Singular Values of Symmetric Matrices. J Math Sci 262, 36–41 (2022). https://doi.org/10.1007/s10958-022-05798-9
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DOI: https://doi.org/10.1007/s10958-022-05798-9