Let $N$ be a matrix in $M_{n}(\mathbf{R})$. Give the factored form of $\chi_{N}$ in $\mathbf{C}[X]$, specifying in the notation the real roots and the complex conjugate roots. Deduce that if $N$ is semi-simple then it is similar in $M_{n}(\mathbf{R})$ to an almost diagonal matrix.