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June 11th, 2018, 05:07 PM   #1
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Invariant Subspaces

Let P be the (hermitian) projection operator onto a subspace M. Show
that 1 − P projects onto M⊥. Hint: You need to show that <m|P|a> = <m|a>
for arbitrary |a> ∈ V and |m> ∈ M; therefore, consider (<m|P|a>)∗, and use the hermiticity of P.
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