A note on definition of matrix convex functions

被引：8
|
作者：
Tikhonov, Oleg E. [1 ]
机构：
[1] Kazan VI Lenin State Univ, Res Inst Math & Mech, Kazan 420008, Russia
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2006年 / 416卷 / 2-3期
基金：
俄罗斯基础研究基金会;
关键词：
matrix convex function; the Neumark theorem;
D O I：
10.1016/j.laa.2005.12.019
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove that a real-valued function f defined on an interval S in R is matrix convex if and only if for any natural k, for all families of positive operators {A(i)}(k)(i=1) in a finite-dimensional Hilbert space, such that Sigma(k)(i=1) A(i)=1, and arbitrary numbers x(i) is an element of S, the inequality [GRAPHICS] holds true. (c) 2006 Elsevier Inc. All rights reserved.
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页码：773 / 775
页数：3
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