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Variational principles for symplectic eigenvalues

, Tanvi Jain
Published in Cambridge University Press
Volume: 64
Issue: 3
Pages: 553 - 559

If A is a real 2n×2n positive definite matrix, then there exists a symplectic matrix M such that MTAM=diag(D,D), where D is a positive diagonal matrix with diagonal entries d1(A)⩽⋯⩽dn(A). We prove a maxmin principle for dk(A) akin to the classical Courant–Fisher–Weyl principle for Hermitian eigenvalues and use it to derive an analogue of the Weyl inequality di+j−1(A+B)⩾di(A)+dj(B).

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JournalData powered by TypesetCanadian Mathematical Bulletin
PublisherData powered by TypesetCambridge University Press
Open AccessNo