Yuan's alternative theorem and the maximization of the minimum eigenvalue function

  • J. E. Martinez-Legaz
  • A. Seeger
Technical Note

Abstract

LetA1 andA2 be two symmetric matrices of ordern×n. According to Yuan, there exists a convex combination of these matrices which is positive semidefinite, if and only if the functionxRn ↦ max {xTA1x,xTA2x} is nonnegative. We study the case in which more than two matrices are involved. We study also a related question concerning the maximization of the minimum eigenvalue of a convex combination of symmetric matrices.

Key Words

Alternative theorems quadratic forms 

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Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • J. E. Martinez-Legaz
    • 1
  • A. Seeger
    • 2
  1. 1.Department d'Economia i d'Història EconòmicaUniversitat Autònoma de BarcelonaBellaterraSpain
  2. 2.Department of MathematicsUniversity of AvignonAvignonFrance

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