I need an algorithm which generates a random matrix with spectral radius equal zero.
The only solution I have so far is to generate two vectors $v,w$, normal onto each other ($v\perp w$), and then take the product $vw^T$. But this is numerically not very stable, and the resulting matrices have spectral radii in the order of $10^{-6}$ for matrices of size $\sim15$.
