In this chapter, we have explored the basic principles of numerical linear algebra—the core of all procedures in scientific computing. The emphasis was first placed on the storage and the basic manipulation of matrices and linear operators. We explored in detail all different factorizations, focusing on their usage to find a solution to matrix equations or eigenvalue problems. All through the chapter, we made it a point to link the functions from the modules scipy.linalg and scipy.sparse to their corresponding routines in the libraries BLAS, LAPACK, ARPACK and SuperLU. For our experiments, we chose interesting matrices from real-life problems that we gathered from the extensive Sparse Matrix Collection hosted by the University of Florida.

In the next chapter, we will address the problems of interpolation and least squares approximation.