eigenvalues of a compact positive definite operator!!!by SVD Tags: compact, definite, eigenvalues, operator, positive 

#1
Dec2012, 09:03 AM

P: 6

Let A be a compact positive definite operator on Hilbert space H.
Let ψ1,...ψn be an orthonormal set in H. How to show that <Aψ1,ψ1>+...+<Aψn,ψn> ≤ λ1(A)+...+λn(A), where λ1≥λ2≥λ3≥..... be the eigenvalues of A in decreasing order. Can someone give me a hint??? 



#2
Dec2012, 10:40 AM

Mentor
P: 10,818

Both the left and right expression look like tr(A).



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