Hi Keita, hope you are doing fine, n=2^18 ... that's quite a big matrix that you got there. Anyway. Yes for n=2^18, the ScaLAPACK pseudo random matrix generator will generate a singular matrix, this is expected. And shifting by one removes the problem, this is expected as well. Please have a look at: Dongarra and Langou. "The Problem With the Linpack Benchmark 1.0 Matrix Generator." International Journal of High Performance Computing Applications, February 2009, vol. 23, no. 1, pp. 5-13. doi: 10.1177/1094342008098683. To generate matrices within the ScaLAPACK framework, I personally use the HPL Benchmark pseudo random matrix generator for several reasons. One of them is that it had the same problem as you mentioned in 1.0 but the problem has been fixed by Piotr Luszczek in 2.0. n=2^18 should be piece of cake for the HPL Benchmark pseudo random matrix generator. Cheers, Julien.