报告人：Olga Kushel 博士（上海交通大学数学系博士后，来自白俄罗斯）

时间：3月25日（周五）下午2点地点：数学楼102报告厅

题目：Scalings and submatrices

摘要：For a positive diagonal matrix  D  and a structured matrix  A, we study diagonal scalings of the form  DA. In this talk, we consider the problem of characterizing the properties of (infinitely many) scalings  DA in terms of the properties of the principal submatrices of A. Since the number of the principal submatrices of an n by n matrix  A is finite, we finally obtain only a finite number of conditions. Our major interest is the case, when all the scalings  DA are Q^2-matrices, since this property leads to positive stability and D-stability of P-matrices. We introduce the property of D_{\theta}-stability, i.e., the stability with respect to a given order theta. For an n by n P-matrix A, we prove a new criterion of D-stability and D_{\theta}-stability, based on the properties of matrix scalings.