Benchmarking Orthonormal Systems - Linear Algebra
Channel: Nick Space Cowboy
Date: 2023-05-01

In this video we benchmark the process of solving random linear systems and orthonormal linear systems in python. This is to show that a linear system containing an orthonormal matrix is consistently solved faster as we scale the dimensions of our linear system. This highlights one of many benefits orthonormal matrices provide us in linear algebra.

Code used in the video: https://github.com/nkphysics/Computational-Linear-Algebra-/tree/master/Unit3/Orthonormal-Matrices

The Gram-Schmidt Process: https://youtu.be/SChiY-2MiWo 

Timestamps:
00:46 - Orthonormal Matrices Overview
01:49 - Benchmarking Methodology
03:54 - Benchmarking Results
06:13 - Why the orthonormal system is faster
09:19 - Conclusion