| MatrixXd X = MatrixXd::Random(5,5); |
| MatrixXd A = X + X.transpose(); |
| cout << "Here is a random symmetric matrix, A:" << endl << A << endl; |
| X = MatrixXd::Random(5,5); |
| MatrixXd B = X * X.transpose(); |
| cout << "and a random postive-definite matrix, B:" << endl << B << endl << endl; |
| |
| GeneralizedSelfAdjointEigenSolver<MatrixXd> es(A,B); |
| cout << "The eigenvalues of the pencil (A,B) are:" << endl << es.eigenvalues() << endl; |
| cout << "The matrix of eigenvectors, V, is:" << endl << es.eigenvectors() << endl << endl; |
| |
| double lambda = es.eigenvalues()[0]; |
| cout << "Consider the first eigenvalue, lambda = " << lambda << endl; |
| VectorXd v = es.eigenvectors().col(0); |
| cout << "If v is the corresponding eigenvector, then A * v = " << endl << A * v << endl; |
| cout << "... and lambda * B * v = " << endl << lambda * B * v << endl << endl; |
