Juba5723 is actually singular (not just numerically singular). The rest appear to have really bad condition numbers; unclear whether they are singular in real life, or just numerically very sensitive. As they are often used to test algorithms designed for stable systems, we should add alternative shifted problems. See also https://morwiki.mpi-magdeburg.mpg.de/morwiki/index.php/Power_system_examples -- K. Lund + J. Saak