INEQUALITIES FOR SEMI-CONVEX MATRIX FUNCTIONS

[摘要] f defined on the set T of matrices with values in the set of matrices is said to be semi-convex if X, Y is-an-element-of T, X less-than-or-equal-to Y implies that lambdaX + (1 - lambda) Y is-an-element-of T, 0 < lambda < 1, and f(lambdaX + (1 - lambda) Y) less-than-or-equal-to lambdaf(X) + (1 - lambda)f(Y). Here X less-than-or-equal-to Y means that every element of Y - X is nonnegative. In this paper, a number of different inequalities are given for semi-convex functions of matrices. (C) 1994 Academic Press, Inc.

[发布日期] 1994-07-15