Linear Algebra and the C Language/a0oe

__NOTOC__ The matrix A and the inverse matrix of A have the same eigenvectors but arranged in reverse order Copy/Paste into the octave window % Properties of spectral decomposition: % % To calculate the spectral decomposition of a symetric matrix A, we need: % % b: The columns of the eigenvectors of A % r: The rows of eigenvectors of the inverse of A % % The eigenvectors of the inverse of A are identical to % the eigenvectors of A but not in the correct order. (Try the example) % % To obtain the eigenvector rows of the inverse of A, % I will take the transpose of the eigenvectors of A, % since A and the inverse of A have the same eigenvectors, % only when A is symetric. clear, clc A = round(10*randn(3)); %% A matrix 3x3 A = A'*A; %% A symetric matrix invA = inv(A); % Eigenvectors, Eigenvalues of A [AEvectors,AEvalues] = eigs(A); % Eigenvectors, Eigenvalues of inverse of A [invAEvectors,invAEvalues] = eigs(invA); AEvectors invAEvectors %%