Inequality on inner product

  • Thread starter marcosdnm
  • Start date
  • #1
1
0
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?
 

Answers and Replies

  • #2
22,089
3,297
Maybe try to diagonalize Q?
 

Related Threads on Inequality on inner product

  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
10
Views
3K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
4
Views
862
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
2
Views
5K
  • Last Post
Replies
1
Views
3K
Top