Jordan Normal Form Question, Linear Algebra?

Both answers are Jordan forms for the original matrix. A Jordan form is only unique up to rearrangement of the Jordan blocks. Your matrix has two blocks 2 and 2 1 0 2.

The difference comes from the order in which the generalized eigenvectors were put into the transfromation matrix. The convention is typically to put the block in ascending order by the modulus of the eigenvavlues--upper left block for the smallest, down to the lowest right block for the biggest. But all of your eigenvalues have the same value, so it's a toss up as to which block should go first.

So again, both are correct Jordan forms. Both can be used in any application you might have. Just be sure that which ever you choose, you use the corresponding transformation matrix.

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