A note on quadratic forms

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Article ID:	iaor20002338
Country:	Germany
Volume:	86
Issue:	1
Start Page Number:	187
End Page Number:	197
Publication Date:	Jan 1999
Journal:	Mathematical Programming
Authors:	Yuan Y., Chen X.

Abstract:

We extend an interesting theorem of Yuan for two quadratic forms to three matrices. Let C1, C2, C3 be three symmetric matrices in ℜ^n×n, if max{x^T C1x, x^T C2x, x^T C3x} ≥ 0 for all x ∈ ℜⁿ; it is proved that there exist ti ≥ 0 (i = 1, 2, 3) such that ∑³i = 1 ti =1 and ∑³i = 1 tiC1 has at most one negative eigenvalue.

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