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Zapiski Nauchnykh Seminarov POMI, 2021, Volume 504, Pages 61–69 (Mi znsl7111)  
Symplectic eigenvalues and singular values of symmetric matrices

Kh. D. Ikramova, A. M. Nazarib

a Lomonosov Moscow State University
b Arak University
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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.
Received: 01.09.2021
Document Type: Article
UDC: 512.643
Language: Russian
Citation: Kh. D. Ikramov, A. M. Nazari, “Symplectic eigenvalues and singular values of symmetric matrices”, Computational methods and algorithms. Part XXXIV, Zap. Nauchn. Sem. POMI, 504, POMI, St. Petersburg, 2021, 61–69
Citation in format AMSBIB
\Bibitem{IkrNaz21}
\by Kh.~D.~Ikramov, A.~M.~Nazari
\paper Symplectic eigenvalues and singular values of symmetric matrices
\inbook Computational methods and algorithms. Part~XXXIV
\serial Zap. Nauchn. Sem. POMI
\yr 2021
\vol 504
\pages 61--69
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl7111}
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