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(a) Let V be a real inner product space. Show that the set of self-adjoint operators on V isa subspace of L(V). (b) Let V be a nonzero complex inner product space. Show that the set of self-adjoint operators on V is not a subspace of L(V). Hint to (b): the identity operator I is self-adjoint, but you can find a scalar z e C suchthat z ·I is not self-adjoint.

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