General¶
This routine computes the in-place inverse of a general fully-populated (invertible) matrix \(A\) as
\[A^{-1} = U^{-1} L^{-1} P,\]
where \(PA=LU\) is the result of LU factorization with partial pivoting. The algorithm essentially factors \(A\), inverts \(U\) in place, solves against \(L\) one block column at a time, and then applies the row pivots in reverse order to the columns of the result.