Gram-Schmidt Process: Orthogonal Vectors & Bases

This lecture covers the Gram-Schmidt process in linear algebra, which generates a sequence of orthogonal vectors from a linearly independent set. The process ensures that the resulting vectors are pairwise orthogonal, non-zero, and linearly independent. It also shows that the span of the original vectors is equal to the span of the orthogonal vectors. Through examples, the instructor demonstrates how to find an orthonormal basis for a given subspace and express a vector in terms of this basis. The lecture concludes with a discussion on expressing a vector in a given orthonormal basis.