Diagonalizability Criterion

This lecture covers the criterion for diagonalizability of matrices, focusing on comparing examples and understanding the relationship between algebraic and geometric multiplicities of eigenvalues. The instructor discusses the conditions under which a matrix is diagonalizable and provides a proof sketch. The lecture emphasizes the importance of factorization of characteristic polynomials and the existence of a basis of eigenvectors. Key concepts include the diagonalizability theorem and the relationship between algebraic and geometric multiplicities of eigenvalues.