Cholesky Decomposition - Computational Linear Algebra
Channel: Nick Space Cowboy
Date: 2022-03-28

All code for this episode can be found on the following GitHub page.
GitHub Repo Directory: https://github.com/nkphysics/Computational-Linear-Algebra-/tree/master/Unit1/7_Cholesky

In this 7th video in this computational linear algebra series we cover a higher level variant of the LU Decomposition called the Choleksy Decomposition. The Choleksy decomposition's key benefit is that there we will only need to keep track of one lower triangular matrix, generally referred to as the Cholesky Factor. If we need to get back to our original matrix we can just multiply our lower triangular matrix (Cholesky Factor) by its transpose. By keeping track on only one matrix (the Choleksy Factor) we greatly improve out performance computationally.
The one key initial condition which allows us to do a Cholesky decomposition though is that our matrix we want to decompose must be considered "positive definite."
For more information on positive definiteness please see the following online resources:
MIT Mini Lecture #1 : https://youtu.be/ojUQk_GNQbQ
MIT Lecture: https://youtu.be/xsP-S7yKaRA
MIT Mini Lecture #2: https://youtu.be/lpnY5QVjU5w
Quick Tutorial on checking positive definiteness: https://youtu.be/ttMZB5Gm_fM