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Some inequalities for eigenvalues and symplectic eigenvalues of positive definite matrices
Published in World Scientific Publishing Co. Pte Ltd
Volume: 30
Issue: 11
We show that for any two n × n matrices X and Y we have the inequality sj2(I + XY) ≤ λ j((I + X∗X)(I + Y∗Y)), where sj(T) and λj(T) denote the decreasingly ordered singular values and eigenvalues of T. As an application, we show that for 2n × 2n real positive definite matrices the symplectic eigenvalues dj, under some special conditions, satisfy the inequality dj(A + B) ≥ dj(A) + d1(B). © 2019 World Scientific Publishing Company.
About the journal
JournalInternational Journal of Mathematics
PublisherWorld Scientific Publishing Co. Pte Ltd