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I try to invert a badly conditioned 8x8 matrix trough the normal Inverse[M] command I receive the bad conditioning warning message, telling me that significant numerical errors could be made. Indeed this is the case as M.M^-1 is not an Identity matrix at all. When I use PseudoInverse[M] I don't get the warning (that's normal), but I don't get a correctly inverted matrix. M.M^-1 is also not identity at all. I did chop the resulst of M.M^-1 but I have very big numbers outside of the diagonal in the first case and numbers of the order of 10^-2 in the PseudoInverse case. The matrix is correctly inverted in another system, but I would like to do everything in Mathematica as my whole program is in Mathematica. What should I do?