Gram-Schmidt Process: Orthogonal Vectors

This lecture covers the Gram-Schmidt process in linear algebra, focusing on constructing orthogonal vectors from a given set in a vector space with a scalar product. The process involves iteratively subtracting projections of vectors onto previously constructed ones. The lecture demonstrates how to create an orthogonal set of vectors and proves their orthogonality. An example in R4 with the standard scalar product illustrates the application of the Gram-Schmidt process step by step, showcasing the computation of orthogonal vectors. The lecture emphasizes the importance of this process in various mathematical applications.