Chapter 5 Matrix Factoring
Matrices have appeared throughout previous chapters and has many uses. In this chapter, we will take a matrix $A$ and write it as the product of two or more matrices. In each case, we will show the purpose of doing this. In each case, the factored matrices will have desirable properties. The first factorization technique that we will examine is called LU factorization, which writes $A=LU$, where $L$ is a lower triangular matrix and $U$ is upper triangular. This factorization will be helpful for solving $A\textbf{x}=\textbf{b}$ repeatedly and can be helpful for finding the inverse of a matrix. We will also see the Singular Value Decomposition (SVD) of a matrix which is quite useful in finding matrices that are close to the original matrix with a smaller rank. We’ll explain why this is important with some nice applications.
