Let K be the operator defined by K = | phi> <psi |, where | phi> and | psi > are two vectors of the state space.
(a) Under what conditions is K Hermitian?
(b) Calculate K^2. Under what condition is K a projector?
(c) Show that K can always be written in the form K=lamba*P1P2 where lamba is a constant to be calculated and P1 and P2 are projectors.
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The solution shows how to write an operator in terms of projection operators and the conditions for a projection operator.