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%% Eigenvalues and Eigenvectors of Matrix %% % Use |gallery| to create a circulant matrix. A = gallery('circul',3) %% % Calculate the eigenvalues and right eigenvectors of |A|. [V,D] = eig(A) %% % Verify that the results satisfy |A*V = V*D|. A*V - V*D %% % Ideally, the eigenvalue decomposition satisfies the relationship. Since % |eig| performs the decomposition using floating-point computations, then % |A*V| can, at best, approach |V*D|. In other words, |A*V - V*D| is close % to, but not exactly, |0|.