Diagonalization of Matrices

This lecture delves into the concept of diagonalization of matrices, focusing on eigenvalues and eigenvectors. The instructor explains the conditions for a matrix to be diagonalizable, the importance of eigenvalues, and the process of finding eigenvectors. Through examples, the lecture covers the calculation of characteristic polynomials, determining linearly independent eigenvectors, and understanding the geometric and algebraic multiplicities of eigenvalues. The lecture also explores the relationship between the dimensions of eigenspaces and the diagonalizability of matrices, emphasizing the significance of bases and subspaces in the context of linear algebra.