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eigenvalues of a compact positive definite operator!
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?
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?