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Inequality on inner product

  1. Jul 17, 2012 #1
    Let x be in R^n and Q in Mat(R,n) where Q is hermitian and negative definite. Let (.,.) be the usual euclidian inner product.

    I need to prove the following inequality:

    (x,Qx) <= a(x,x)

    where "a" is the maximum eigenvalue of Q.

    Any idea?
  2. jcsd
  3. Jul 17, 2012 #2
    Maybe try to diagonalize Q?
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