Generalized interlacing inequalities

Abstract

We discuss some applications of generalized interlacing inequalities of Ky Fan to the study of (a) some classical matrix inequalities and (b) matrix problems in quantum information science.

Keywords:

• Hermitian matrices
• eigenvalues
• interlacing inequalities
• numerical ranges

AMS Subject Classifications::

• 15A18
• 15A57
• 15A60
• 15A90

Acknowledgements

This research was done when C.-K. Li was visiting the Department of Mathematics, Hong Kong University of Science and Technology under a Fulbright Fellowship in 2011. Li is an honorary professor of the University of Hong Kong, Taiyuan University of Technology, and Shanghai University. His research was supported by an NSF grant, a HK RGC grant, and the Shanxi 100 talent program. Research of Y.-T. Poon was supported by an NSF grant. Research of N.-S. Sze was supported by a HK RGC grant.