Write the matrix equation (Amathbf{v}=lambdamathbf{v})
Rearrange to ((A-lambda I)mathbf{v}=0)
Find the eigenvalues (lambda) by solving (det(A-lambda I)=0)
Substitute each eigenvalue into ((A-lambda I)mathbf{v}=0)
Solve the resulting homogeneous system for a nonzero vector (mathbf{v})
Any nonzero solution (mathbf{v}) is an eigenvector
Scale the eigenvector by any nonzero constant if needed
Repeat for each eigenvalue to find all eigenvectors