Find the eigenvalues of the matrix (A) by solving (det(A-lambda I)=0)
For each eigenvalue (lambda), form the matrix (A-lambda I)
Solve ((A-lambda I)mathbf{v}=0) for a nonzero vector (mathbf{v})
The nonzero solutions (mathbf{v}) are the eigenvectors corresponding to (lambda)
Write the eigenvectors as the null space of (A-lambda I)
Verify each eigenvector by checking (Amathbf{v}=lambdamathbf{v})