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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???

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# Eigenvalues of a compact positive definite operator

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