Orthogonality and Least Squares Methods

This lecture delves into the concepts of orthogonality and least squares methods, focusing on solving linear systems where the solution is not exact but close to the desired result. The instructor explains the geometric notions necessary to understand distance and proximity in arbitrary-dimensional vector spaces, emphasizing the use of norms and inner products. The lecture covers the definition of norm, distance, and angle between vectors, illustrating how these concepts are crucial in determining closeness and optimality in vector spaces. Additionally, the lecture explores orthogonal subspaces and their properties, providing insights into the relationships between subspaces and their orthogonal complements.