Orthogonal Linear Maps

This lecture introduces the concept of orthogonal linear maps in Euclidean spaces, defining them as linear maps where the norm of the image of the zero vector equals zero. The properties of orthogonal matrices are explored, including forming orthonormal bases and having a determinant of +1. The lecture also covers the invertibility of orthogonal maps and the equivalence of various conditions for a matrix to be orthogonal. Additionally, it discusses the least squares solution of linear equations and the uniqueness of solutions in the context of orthogonal matrices.