A note on quadratic forms

被引：17
|
作者：
Chen, X [1 ]
Yuan, YX [1 ]
机构：
[1] Chinese Acad Sci, Inst Computat & Sci Engn Comp, Lab Sci & Engn Comp, Beijing 100080, Peoples R China
来源：
MATHEMATICAL PROGRAMMING | 1999年 / 86卷 / 01期
关键词：
quadratic forms; convex combination; matrix perturbation;
D O I：
10.1007/s101070050085
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
We extend an interesting theorem of Yuan [12] for two quadratic forms to three matrices. Let C-1, C-2, C-3 be three symmetric matrices in R-nxn, if max{x(T) C(1)x,x(T) C(2)x, x(T) C(3)x} greater than or equal to 0 for all x is an element of R-n, it is proved that there exist t(i) greater than or equal to 0 (i = 1, 2, 3) such that Sigma(i=1)(3) t(i)C(i) has at most one negative eigenvalue.
引用
收藏
页码：187 / 197
页数：11
相关论文
共 50 条
12345