Start with the matrix (A) and each eigenvalue (lambda)
Form the matrix (A – lambda I)
Solve the homogeneous system ((A – lambda I)mathbf{v} = mathbf{0})
Find the nonzero solutions (mathbf{v}) in the null space of (A – lambda I)
Express the solution vector(s) in parametric form if needed
Choose any nonzero vector from the solution set as an eigenvector
Repeat for each eigenvalue
Optionally scale each eigenvector to a convenient form or normalize it