Matrix majorizations and their applications
The notion of a vector majorization arose independently in a variety of contexts in the early 20th century. These contexts are Muirhead’s inequality, economical contexts (the Lorenz curve and Dalton principle), linear algebra (Schur’s work on the Hadamard inequality), and many others. There are several ways to extend the notion of vector majorizations to matrices. Different types of matrix majorizations have been motivated by different applications in the theory of statistical experiments, economics, stochastic matrices, and others. The modern theory of matrix majorization is related to linear algebra, linear optimization, statistics, convex geometry, and combinatorics.
The talk will cover several aspects of the theory of majorizations, including our recent results. In particular, we discuss majorization for matrix classes motivated by applications to the theory of statistical experiments, a problem of finding minimal cover classes, restricts of majorizations to (0,1)-matrices and (0,1,-1)-matrices, which leads to a wide range of combinatorial results, and linear preserver problems.
Meeting ID: 878 5613 2062
תאריך עדכון אחרון : 24/07/2022