國立清華大學 數學系

Abstract：
Horn's problem is a deceptively simple question in linear algebra: 
if A and B are two Hermitian matrices with given spectra, what are the possible spectra of A+B? After nearly a hundred years of work by many mathematicians, a complete solution to Horn's problem was finally proved at the turn of the 21st century. This talk will start with an overview of the classical Horn's problem and its solution. I will then discuss recent results on two generalizations of the problem: a probabilistic version for random matrices, and an infinite-dimensional version for operators on a Hilbert space.