Change of Basis: Motivation

This lecture covers the concept of change of basis in linear algebra, focusing on the motivation behind it. The instructor explains the orthogonal symmetry with respect to a specific line equation in R2, illustrating the transformation using matrices. The lecture also revisits the projection operation and demonstrates how to perform a change of basis using a given basis. Additionally, the lecture introduces the concept of symmetry orthogonal to a line equation and provides examples of applying this transformation. The importance of selecting an appropriate basis for efficient computations is emphasized throughout the lecture.