Find the eigenvalues by solving ( det(A-lambda I)=0 )
For each eigenvalue ( lambda ), form the matrix ( A-lambda I )
Solve the homogeneous system ( (A-lambda I)mathbf{v}=0 )
Find the nonzero vectors ( mathbf{v} ) in the null space of ( A-lambda I )
Any nonzero scalar multiple of an eigenvector is also an eigenvector
If an eigenvalue is repeated, solve ( (A-lambda I)mathbf{v}=0 ) once and determine all independent eigenvectors from the solution space
Verify each eigenvector by checking ( Amathbf{v}=lambda mathbf{v} )