Gram-Schmidt Process

This lecture covers the Gram-Schmidt orthogonalization process, which is a method to find an orthogonal basis for a vector subspace. Starting with a basis, the process involves iteratively constructing orthogonal bases and ensuring orthogonal projections on vector subspaces. The lecture explains the step-by-step procedure, including optional steps for simplification and normalization to obtain an orthonormal basis. Through examples and theorems, the instructor demonstrates how to apply the Gram-Schmidt process effectively in practice.