The method for symbolic computation of eigenvectors and eigenvalues involves first finding the eigenvalues from the characteristic polynomial:
det(M - λ I) = 0
where, in this case for three dimensional matrix M =
| m00 | m01 | m02 |
| m10 | m11 | m12 |
| m20 | m21 | m22 |
which gives the characteristic equation:
-λ³ + λ²(m00 + m11 + i) + λ(m01 m10 + m02 m20 + m21 m12 - m00 m11 - i m00 - i m11) + (m00 m11 i - m00 m12 m21 - m01 m10 i + m10 m02 m21 + m20 m01 m12 - m20 m02 m11) = 0
We then need to solve this cubic equation to give uto 3 values of λ.
We can then substitute these into
|
= |
|
which is equivalent to solving 3 simultaneous equations.
