Eigenvalues:
Eigenvectors corresponding to satisfy
Solving using Gaussian elimination:
The general solution space is:
We choose v1z=1 to get
Eigenvectors corresponding to satisfy
Solving using Gaussian elimination:
The general solution space is:
We can use the two vectors above, which means choosing v2y=1 and v2z=0 for one, and v2y=0 and v2z=1 for the other. That gives
If the three vectors ,
, and
are
used as basis, A becomes diagonal. So despite the multiple root,
this A is still diagonalizable. But if the solution space for the
second eigenvalue would have been one-dimensional, the matrix would
not have been diagonalizable.
y