LU Decomposition - Computational Linear Algebra
Channel: Nick Space Cowboy
Date: 2022-01-18

In this fifth video we cover the LU decomposition, which plays a crucial role in understanding how we can solve a linear system computationally. To do the LU decomposition we utilize the Gaussian Elimination algorithm we discussed in the fourth episode. If you need a refresher here is a link to that video.
https://youtu.be/59TAcVWZ0LY

The LU decomposition is a specific configuration of a matrix decomposition that allows us to show that the solutions to the upper triangular system we get from structured Gaussian elimination satisfy the original linear system Ax=b. We explore the LU decomposition computationally in the octave an python languages, utilizing numpy and scipy. In particular we cover how to do a lu decomposition in python both with numpy and without numpy. For those matlab users octave is a very similar free and open source language, so matlab users will be able to quickly adapt any of the octave code to matlab, and vice versa.
This episodes directory in the series repo can be found in the following links.

Github: 
https://github.com/nkphysics/Computational-Linear-Algebra-/tree/master/Unit1/5_LU_Decomposition
https://gitlab.com/n_space_cowboy/computational-linear-algebra/-/tree/master/5_LU_Decomposition
Understanding the lu decomposition if also crucial for understanding other matrix decomposition since it is one of the more general matrix decompositions.

If you have any comments, questions or concerns feel free to let me know in the comment section.