I have a system of equations that I am trying to solve. In matrix form, it's written as
$$x(I - S) = b.$$
I am solving for $x$, where $I$ is the identity matrix and $S$ is a matrix where each column sums up to one. $b$ is strictly positive.
Now, unfortunately, the determinant of $I - S$ is very small. Inverting it leads to a matrix that is huge everywhere, and even
numpy.linalg.solve comes up with a solution for $x$ that is huge (every element around e+19). What is an alternative way of solving this? The matrix itself is not large, there are around 30-50 elements in $x$.