Block diagonalization of a matrix

[Qturtle]

Hi. i have a 4x4 matrix
\begin{pmatrix}
0 & 1 & 1 & 1\\
1 & 0 & i & -i\\
1 & -i & 0 & i\\
1 & i & -i & 0\\
\end{pmatrix}
it has 2 eigenvalues
and i want to block diagonalize it into a 2x2 block diagonal matrix.
i can't seem to find the proper way to do that. do i need to have a commuting matrix in order to preform block diagonalization?
iv'e tried to follow this
http://en.wikipedia.org/wiki/Jordan_normal_form
but the square of the matrix gives me the same matrix with a constant factor, so i don't get any new equation for the eigenvectors.

 

[Stephen Tashi]

iv'e tried to follow this
http://en.wikipedia.org/wiki/Jordan_normal_form

This morning, the top hit in Google for such an algorithm is the PDF: http://math.rice.edu/~friedl/math355_fall04/Jordan.pdf