Form the characteristic matrix (A – lambda I)
Compute the determinant (det(A – lambda I))
Set the characteristic polynomial equal to zero
Solve (det(A – lambda I) = 0) for (lambda)
The solutions are the eigenvalues
For a (2 times 2) matrix (begin{pmatrix} a & b \ c & d end{pmatrix}), solve ((a-lambda)(d-lambda)-bc=0)
For a (3 times 3) or larger matrix, expand the determinant and solve the resulting polynomial
Check each eigenvalue by substituting it back into ((A – lambda I)mathbf{v} = mathbf{0}) if needed