If the eigenvalue a n has degenerate, orthonormal eigenvectors { | a n 1 ⟩ ⟩ , | a n 2 ⟩ ⟩ , … … , | a n m ⟩ ⟩ } , then the projection operator onto the eigensubspace can be defined as the identity operator in the eigensubspace: P n = | a n 1 ⟩ ⟩ ⟨ ⟨ a n 1 | + | a n 2 ⟩ ⟩ ⟨ ⟨ a n 2 | + ⋯ ⋯ + | a n m ⟩ ⟩ ⟨ ⟨ a n m | , and then P ( a n ) = tr ⁡ ⁡ ( P n ρ ρ ) .