inequality on inner product

marcosdnm

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?

micromass

Maybe try to diagonalize Q?

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marcosdnm	inequality on inner product Tweet 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?

micromass Blog Entries: 8 Recognitions: Gold Member Science Advisor Staff Emeritus	Maybe try to diagonalize Q?