Citation
X. Chen et Yx. Yuan, A note on quadratic forms, MATH PROGR, 86(1), 1999, pp. 187-197
Citations number
13
Categorie Soggetti
Mathematics
Journal title
MATHEMATICAL PROGRAMMING
ISSN journal
00255610
→ ACNP
Volume
86
Issue
1
Year of publication
1999
Pages
187 - 197
Database
ISI
SICI code
0025-5610(199909)86:1<187:ANOQF>2.0.ZU;2-8
Abstract
We extend an interesting theorem of Yuan [12] for two quadratic forms to th
ree matrices. Let C-1, C-2, C-3 be three symmetric matrices in R-nxn, if ma
x{x(T) C(1)x,x(T) C(2)x, x(T) C(3)x} greater than or equal to 0 for all x i
s an element of R-n, it is proved that there exist t(i) greater than or equ
al to 0 (i = 1, 2, 3) such that Sigma(i=1)(3) t(i)C(i) has at most one nega
tive eigenvalue.