Jordan canonical form for a matrix

How do I find the Jordan canonical form and its transitions matrix of this matrix?

$$\begin{pmatrix}1&0&0&0\\0&0&1&0\\0&1&0&0\\0&0&0&1\end{pmatrix}$$

The characteristic polynomial is $$(x+1)(x-1)^3$$ and the eigenvectors are for $$x=1$$ we have $$(0,0,0,1)$$, $$(0,1,1,0)$$, $$(1,0,0,0)$$ and for the $$x=-1$$ we have $$(0,-1,1,0)$$.

• HINT: For each eigenvalue, the geometric multiplicity agrees with the algebraic multiplicity. – vadim123 Dec 8 '13 at 21:00
• Check the minimal pol. of the matrix is $\;(x-1)(x+1)\;$ and thus it is diagonalizable, what makes its JCF pretty boring...and simple. – DonAntonio Dec 8 '13 at 21:05

$$J = \left[ \begin{array}{rrrr} -1 & 0 & 0 & 0\\ 0 & 1 & 0 & 0\\ 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 1 \end{array} \right]$$