18.085 Computational Science and Engineering I, Fall 2008. 18.085 Computational Science and Engineering I, Fall 2008. Lecture 22: Diagonalization and powers of A. 32.8 Computing Eigenvalues and Eigenvectors. 32.8 Computing Eigenvalues and Eigenvectors. 4.6 Eigenvalues and the Characteristic Equation of a Matrix. Lecture 21: Eigenvalues and eigenvectors.