Diagonalization of Linear Maps

This lecture covers the concept of diagonalization of linear maps, focusing on the diagonalization of a linear map by finding a basis formed by eigenvectors. The instructor explains the conditions for a linear map to be diagonalizable and demonstrates the process through examples. The lecture also discusses the geometric and algebraic multiplicities of eigenvalues, illustrating how to determine if a linear map is diagonalizable. Additionally, the lecture explores the configurations of proper subspaces and the study of possible cases when diagonalizing a linear map.