The Eigenvalues of the Pauli spin matrices are ±1. We now evaluate the corresponding Eigenvectors that we denote as |±>.

Matrix σ_z:

The Eigenvectors of σ_z must satisfy the conditions

Matrix σ_x:
The Eigenvectors of σ_x must satisfy the conditions

Matrix σ_y:
The Eigenvectors of σ_y must satisfy the conditions

.....