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%% Left Eigenvectors %% % Create a 3-by-3 matrix. A = [1 7 3; 2 9 12; 5 22 7]; %% % Calculate the right eigenvectors, |V|, the eigenvalues, |D|, and the left % eigenvectors, |W|. [V,D,W] = eig(A) %% % Verify that the results satisfy |W'*A = D*W'|. W'*A - D*W' %% % Ideally, the eigenvalue decomposition satisfies the relationship. Since % |eig| performs the decomposition using floating-point computations, then % |W'*A| can, at best, approach |D*W'|. In other words, |W'*A - D*W'| is % close to, but not exactly, |0|.