Each of the (Hermitian) Pauli matrices of spin- ⁠ 1 / 2 ⁠ particles has two eigenvalues, +1 and −1. The corresponding normalized eigenvectors are ψ ψ x + = | 1 2 , + 1 2 ⟩ x = 1 2 ( 1 1 ) , ψ ψ x − − = | 1 2 , − − 1 2 ⟩ x = 1 2 ( 1 − − 1 ) , ψ ψ y + = | 1 2 , + 1 2 ⟩ y = 1 2 ( 1 i ) , ψ ψ y − − = | 1 2 , − − 1 2 ⟩ y = 1 2 ( 1 − − i ) , ψ ψ z + = | 1 2 , + 1 2 ⟩ z = ( 1 0 ) , ψ ψ z − − = | 1 2 , − − 1 2 ⟩ z = ( 0 1 ) .