Diagonalizability of Linear Transformations

This lecture covers the concept of diagonalizability of linear transformations, focusing on the conditions for a matrix to be diagonalizable and the properties associated with it. It explains the process of finding a base of eigenvectors, determining the geometric and algebraic multiplicities of eigenvalues, and the implications of diagonalizability in terms of linear independence and dimensionality. The lecture also discusses examples and corollaries related to diagonalizability, including the significance of distinct eigenvalues and the existence of a diagonal matrix. Additionally, it explores the relationship between diagonalizability and the number of linearly independent eigenvectors.