I know the historical importance of the link between linear systems and determinants. I also know that determinants have a beautiful connection with non-singular matrices, i.e., if a matrix is non-singular its determinant is not zero. Furthermore, determinants can be used to characterize the critical points of a $C^2$ function. However, it seems that determinants are not used in these situations anymore at least in numerical computation.
Are there practical situations that determinants are still used in numerical simulation?