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

页码：187 / 197

页数：11

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