Orthogonality and Least Squares Method

This lecture delves into the concepts of orthogonality and the method of least squares, focusing on solving linear equation systems where the solution is close to but not exactly equal to the desired result. The instructor explains the geometric notions necessary to discuss distance and proximity in arbitrary-dimensional vector spaces, particularly in Rn. The lecture covers the definition of the dot product, properties of the dot product, and the concept of vector norms. It also explores the normalization of vectors to unit vectors, the calculation of distances between vectors, and the definition of angles between vectors. The Pythagorean theorem is generalized to define the angle between two vectors in RN, emphasizing the importance of orthogonality in various mathematical calculations.