Orthogonal Projection: Example and Additional Remarks

This lecture covers the concept of orthogonal projection onto a subspace, illustrated with an example in R4. It explains how to find the orthogonal projection of a vector onto a subspace and how to determine a basis for the subspace. The lecture also discusses the process of finding an orthogonal basis using the Gram-Schmidt procedure, along with corollaries related to the dimensions of subspaces. The importance of orthogonal bases and their applications in vector spaces is highlighted, emphasizing the significance of the projection process.