Matrix Factorization and Solving Linear Systems

Matrix factorization expresses a square matrix $A$ as a product of two triangular matrices: $$A = LU$$ where $L$ is lower triangular (with unit diagonal in Doolittle's method) and $U$ is upper triangular. This is called LU decomposition. $$A = \begin{bmatrix} 1 & 0 & 0 \ l{21} & 1 & 0 \ l{31} &...