Orthogonal Diagonalization

This lecture covers the concept of orthogonal diagonalization of a symmetric matrix through the use of orthonormal bases. It explains how to determine the characteristic polynomial of a matrix, find its distinct roots, and orthogonalize it using the Gram-Schmidt method. The process of finding an orthonormal basis and diagonalizing the matrix is detailed step by step, emphasizing the importance of using an orthogonal basis. The lecture also delves into the properties of symmetric matrices and the conditions under which a matrix can be orthogonally diagonalized.