How To Find Eigenvectors Of A Matrix?

Find the eigenvalues of the matrix by solving the characteristic equation ( 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 solution ( mathbf{v} ) is an eigenvector corresponding to ( lambda )

If needed, scale the eigenvector by any nonzero constant

Repeat the process for each eigenvalue