1 MatrixXd X = MatrixXd::Random(5,5); 2 MatrixXd A = X + X.transpose(); 3 cout << "Here is a random symmetric 5x5 matrix, A:" << endl << A << endl << endl; 4 5 SelfAdjointEigenSolver<MatrixXd> es(A); 6 cout << "The eigenvalues of A are:" << endl << es.eigenvalues() << endl; 7 cout << "The matrix of eigenvectors, V, is:" << endl << es.eigenvectors() << endl << endl; 8 9 double lambda = es.eigenvalues()[0]; 10 cout << "Consider the first eigenvalue, lambda = " << lambda << endl; 11 VectorXd v = es.eigenvectors().col(0); 12 cout << "If v is the corresponding eigenvector, then lambda * v = " << endl << lambda * v << endl; 13 cout << "... and A * v = " << endl << A * v << endl << endl; 14 15 MatrixXd D = es.eigenvalues().asDiagonal(); 16 MatrixXd V = es.eigenvectors(); 17 cout << "Finally, V * D * V^(-1) = " << endl << V * D * V.inverse() << endl; 18
