Register to reply 
Eigenvalues of a compact positive definite operator 
Share this thread: 
#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: 12,113

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



Register to reply 
Related Discussions  
Positive definite matrix and its eigenvalues  Calculus & Beyond Homework  1  
Positive definite operator/matrix question  Calculus & Beyond Homework  3  
Eigenvalues of positive definite (p.d) matrix  Linear & Abstract Algebra  2  
Inequality involving positive definite operator  Advanced Physics Homework  4  
Eigenvalues of Positive Definite matrices  &MATLAB..  Math & Science Software  3 