Theoretical Statistics and Mathematics Unit, ISI Delhi
For every positive definite matrix of order 2n, there exist n positive numbers associated to it. We call these numbers the symplectic eigenvalues of the matrix. Symplectic eigenvalues are important in different areas such as classical (Hamiltonian) mechanics, quantum information and symplectic topology. Recently there has been a heightened interest in the study of symplectic eigenvalues both by mathematicians and physicists due to their important applications in quantum information. In this talk, we discuss some fundamental inequalities and variational principles involving symplectic eigenvalues, perturbation theorems and relationship between symplectic eigenvalues and ordinary eigenvalues.
This talk is based on a joint work with Rajendra Bhatia.