Matrix majorizations and their applications

Seminar
Speaker
Pavel Shteyner
Date
27/07/2022 - 11:30 - 10:30Add to Calendar 2022-07-27 10:30:00 2022-07-27 11:30:00 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. ================================================ https://us02web.zoom.us/j/87856132062 Meeting ID: 878 5613 2062 Zoom -- see link below אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Zoom -- see link below
Abstract

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.

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https://us02web.zoom.us/j/87856132062

Meeting ID: 878 5613 2062

Last Updated Date : 24/07/2022