A factorization result in linear algebra is a way of decomposing a matrix into the product of (presumably simpler) matrices. We have found such results to be very useful in earlier sections and many more may be found here. We discuss the Schur decomposition, the spectral theorem for normal matrices, the LU and QR and Cholesky decompositions, the singular value decomposition, the Cayley-Hamilton theorem and the Jordan normal form. Sylvester’s law of inertia and the Witt theorems are proved. Properties of quadratic forms and the Frobenius and operator norms are developed as well as condition number and an analysis of error in matrix equations.