國立清華大學 數學系

Abstract:

For any n-by-n complex matrix A, its numerical range W(A) is defined by { x*Ax : x ϵ C^n, x*x=1 }. The study of the numerical range has a history of one hundred years now. It started with the amazing result of Toeplitz-Hausdorff that the numerical range is always a convex set in the plane. In this talk, we start to present some basic properties of the numerical range of a matrix. Then we will introduce some recent results and problems on this topic.