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