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Eigenvalue oscillation of Loewner Matrices

Rajendra Bhatia教授(Indian Statistical Institute,印度)
2016-12-23(周五)15:00-16:00  闵行校区数学楼102报告厅
 
报告人简介:

Bhatia教授是矩阵分析和算子理论领域的著名学者,印度国家科学院和印度科学院两院院士,2016年 Hans Schneider 奖获得者。

报告内容简介:

Let f be a smooth function on the positive half line. For any n, and for any choice of points p_1, p_2, .......,p_n, the matrix with its (i,j) entry equal to the divided difference [ f(p_i) - f(p_j) ] / [p_i - p_j] is called a Loewner matrix associated with f. These matrices are important in several contexts: numerical analysis, complex function theory, differentiation of matrix functions, the theory of matrix monotone functions. A celebrated theorem of C. Loewner says that if f(t) = t^r and 0 < r < 1, then all such matrices are positive definite, and this is not so for other values of r. What happens for these other values of r ? The answer will be provided in this talk.

主持人:詹兴致 教授
   
 
 
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