Chapter 4: LU and PLU decompositions

You will see in this chapter that Gaussian elimination can be interpreted as decomposing the matrix A, or at least a matrix obtained from A by permuting rows, into triangular factors—a lower triangular factor L and an upper triangular factor U. This is a neat theoretical fact, but it is also practically useful. Once you have solved a system Ax = b, you know the decomposition into triangular factors, and, if you wanted to solve another system with the same matrix A, you could use that to make the computation much faster.