Diagonalizable Matrices: Criteria and Applications

This lecture covers the criteria for diagonalizing matrices, including the definition of diagonalizable matrices and the criterion for diagonalization. It also explores examples and practical applications, such as finding eigenvalues and eigenvectors, determining if a matrix is invertible, and understanding the concept of similar matrices. The lecture delves into the importance of eigenvalues, eigenvectors, and the diagonalization process, emphasizing the significance of symmetric matrices. Additionally, it discusses the process of finding eigenspaces and the implications of distinct eigenvalues on diagonalizability.