Description
Normal matrices form a central class in matrix analysis, including Hermitian, skew-Hermitian, and unitary, positive semidefinite, permutation matrices and so on. This presentation surveys fundamental properties of normal matrices, including spectral characterization, unitary diagonalization, and trace (in)equality through majorization. It highlights equivalent conditions for normality, with discussions extending to matrix exponentials and polynomials. Examples and counterexamples are provided to clarify certain subtle points about matrix normality. The talk is based on a recent paper published in JMC (joint work with Y.-J. Hu)
Date of Event
Thursday, April 16, 2026
Location
Parker Building 338
Included in
Normal Matrices
Parker Building 338
Normal matrices form a central class in matrix analysis, including Hermitian, skew-Hermitian, and unitary, positive semidefinite, permutation matrices and so on. This presentation surveys fundamental properties of normal matrices, including spectral characterization, unitary diagonalization, and trace (in)equality through majorization. It highlights equivalent conditions for normality, with discussions extending to matrix exponentials and polynomials. Examples and counterexamples are provided to clarify certain subtle points about matrix normality. The talk is based on a recent paper published in JMC (joint work with Y.-J. Hu)
Presenter Bio
Fuzhen Zhang serves as professor of mathematics at NSU Florida. He earned his Ph.D. in mathematics from the University of California-Santa Barbara (UCSB) in 1993. Dr. Zhang joined NSU in 1993 and has served as mentor and professor to hundreds of NSU students. His research interests include matrix analysis, linear algebra, multilinear algebra and has published more than 90 research papers and about 150 math-related items, including 3 books. He has been on editorial boards of several mathematical journals and an Invited Plenary Speaker at conferences in his research area. He is recipient of NSU Distinguished Professor of the Year Award and Shanghai City "Overseas Renowned Professors (海外名师)" Award. Dr. Zhang was a host/co-advisor of Visiting Professors, Postdocs, and Ph.D. students from Turkey and China