This lecture covers the calculation of characteristic polynomials, eigenvalues, and eigenvectors of matrices A, B, C, D, and E. General methods for finding eigenvalues and eigenvectors are discussed, emphasizing the non-uniqueness of eigenvectors. Specific solutions are provided for each matrix, highlighting the relationship between eigenvalues and eigenvectors. The lecture concludes with a summary of the results obtained for matrices A, B, C, D, and E.