Orthogonal/Orthonormal Bases and Polynomials

This lecture covers the concepts of orthogonal and orthonormal bases, the Gram-Schmidt orthogonalization process, and orthogonal polynomials. The instructor explains the decomposition of vectors on orthogonal bases, the process of building an orthonormal basis, and the application of Gram-Schmidt process to generate orthogonal polynomials. Examples of orthogonal polynomials in physics, such as Legendre, Hermite, and Laguerre polynomials, are discussed. The lecture emphasizes the importance of these polynomials as solutions to differential equations in physical sciences.