# Eigenvalue inequalities of matrix product

## Description

Given two n-by-n complex matrices, one is Hermitian and one is positive semidefinite, all of the n eigenvalues (counting multiplicities) of the product of the given matrices are necessarily real. Selecting any k of the n eigenvalues, we present lower and upper bounds for the sum of these k selected eigenvalues. Our results extend and complement the existing ones.

## Location

Parker Building, Room 301

Eigenvalue inequalities of matrix product

Parker Building, Room 301

Given two n-by-n complex matrices, one is Hermitian and one is positive semidefinite, all of the n eigenvalues (counting multiplicities) of the product of the given matrices are necessarily real. Selecting any k of the n eigenvalues, we present lower and upper bounds for the sum of these k selected eigenvalues. Our results extend and complement the existing ones.

## Presenter Bio

Fuzhen Zhang received his Ph.D. in Mathematics from the University of California-Santa Barbara (UCSB) in 1993. He is currently a full professor of Nova Southeastern University in Fort Lauderdale, Florida, USA. Zhang’s research areas are matrix analysis, linear and multilinear algebra (as well as operator theory and combinatorics). He has published 130 math-related items, including 80 research articles and three books:

Linear Algebra: Challenging Problems for Students(Johns Hopkins University Press),Matrix Theory(Springer), and editor ofThe Schur Complement and Its Applications(Springer). Zhang has served on the editorial boards of several mathematical journals. He has given 80 talks on mathematics worldwide, including Invited Plenary Lecturer at Int’l Conference on Matrix Analysis and its Applications, Bedlewo, Poland, 2017, plenary talk at the 2016 conference on Recent Advances in Linear Algebra and Graph Theory at the University of Tennessee—Chattanooga; plenary talk at the 18th International Linear Algebra Society (ILAS) Conference in Rhode Island in 2013; and as an invited speaker at the 22nd International Workshop on Matrices and Statistics at Fields Institute at the University of Toronto, Canada, in 2013. He has served as Chair or Co-chair of the Scientific Organizing Committee of the serial International Conference on Matrix Analysis and Applications (ICMAA). Zhang received the 2016 Shanghai City Overseas Renowned Professor Award. He is a recipient of the FCAS Distinguished Professor Award (2013) and NSU’s Professor of the Year award (2013). He is one of the founders of the Chinese Association of Science, Education, and Culture (CASEC, established 1994). He served as the Principal of Contemporary Chinese School of South Florida (CCSSF-Broward Campus) 2000-2002. His hobbies are: Playing basketball/volleyball, Sing & Dancing, and Writing essays in Chinese.