basis

Table of Contents 1. Motivation 2. Orthogonalization via Gram-Schmidt 3. Legendre Polynomials 4. Conclusion 5. References All the code used to generate the animations in this article is available at the following public repository: Auxiliary repository 1. Motivation Orthogonal bases are a powerful tool in linear algebra. They allow us to decompose vectors into simpler components, and they are at the core of many numerical algorithms. For instance, imagine we are given an arbitrary function....