Eigenspace

An eigenspace of operator A^\hat{A} is the Set of all eigenvectors/Eigenstate with the same eigenvalue plus the zero vector.

Example

If operator A^\hat{A} has eigenvalue λ\lambda, then the λ\lambda-eigenspace of the operator A^\hat{A} is

{∣ψ⟩:A^∣ψ⟩=λ∣ψ⟩}\{\left\lvert \psi \right\rangle:\hat{A}\left\lvert \psi \right\rangle=\lambda\left\lvert \psi \right\rangle\}