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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 $\sim15$.

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  • $\begingroup$ Are there any other requirements? One way is to just generate a random number for each matrix entry $A_{ij}$ where $i < j$. Then the matrix is upper-triangular and its diagonals are all zero, so it has spectral radius zero. $\endgroup$ – Zach Langley Dec 11 '18 at 20:53

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