Unfortunately, not all matrices are diagonalizable. However, A can always be reduced to the Jordan Canonical form

(1.17)

where each Jordan block has the form

(1.18)

The dimension of the Jordan block corresponds to the multiplicity of the eigen value . Thus, if is simple, the block is a scalar. With this, it is relatively easy to show that is

1.   stable when either ( or and is simple,
2.   asymptotically stable when and
3.   unstable otherwise.