Description
Given a square matrix, one can associate it with a variety of numerical values and properties—such as the trace, determinant, eigenvalues, and singular values (at the undergraduate level), and the numerical range (and numerical radius), matrix norms, and majorization inequalities involving eigenvalues and singular values (at the graduate level). These studies all serve a common goal: to describe and understand the matrix as thoroughly as possible. In this talk, we present several inequalities involving a matrix A and its operator modulus ∣A∣, particularly in the context of their powers acting on the unit sphere (i.e., unit vectors)
Date of Event
Thursday, April 24, 2025
Location
Parker Building 338
Included in
Some inequalities of a matrix and its modulus in powers acting on unit vectors
Parker Building 338
Given a square matrix, one can associate it with a variety of numerical values and properties—such as the trace, determinant, eigenvalues, and singular values (at the undergraduate level), and the numerical range (and numerical radius), matrix norms, and majorization inequalities involving eigenvalues and singular values (at the graduate level). These studies all serve a common goal: to describe and understand the matrix as thoroughly as possible. In this talk, we present several inequalities involving a matrix A and its operator modulus ∣A∣, particularly in the context of their powers acting on the unit sphere (i.e., unit vectors)
Presenter Bio
Dr. Fuzhen Zhang serves as professor of mathematics at NSU Florida. He earned his Ph.D. in mathematics from the University of CaliforniaSanta 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, functional analysis, operator theory, and combinatorics. You can learn more about Dr. Zhang’s expansive work here: https://works.bepress.com/f uzhen-zhang/about/.