Question: (a) Suppose K, M: U U are self-adjoint linear functions on an inner product space U. Prove that (k[u], u) = (M[u], u) for

(a) Suppose K, M: U → U are self-adjoint linear functions on an inner product space U. Prove that (k[u], u) = (M[u], u) for all u ∈ U if and only if K = M.
(b) Explain why this result is false if the self-adjointness hypothesis is dropped.

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