Matrix Factorization

We wish to write a series of blog posts on the different ways one can factorize a matrix.

The goal is to describe how to interpret these matrix decompositions when possible discuss the numerical stability of the algorithms used to generate them.

Posts:

• 2025 Apr 17: The Column-Row factorization $(A = CR)$

We wish to hopefully cover the following factorizations in future posts:

• The LU decomposition
• Eigendecomposition
• SVD
• The QR decomposition
• Cholesky decomposition

Reading list:

• This paper describes a $A = CW^{-1}B$ factorization that it calls “magic”.
• Nick Hingham’s “What is” series of blogposts seem like an incredible resource.