1 MatrixXd A = MatrixXd::Random(6,6); 2 cout << "Here is a random 6x6 matrix, A:" << endl << A << endl << endl; 3 4 EigenSolver<MatrixXd> es(A); 5 cout << "The eigenvalues of A are:" << endl << es.eigenvalues() << endl; 6 cout << "The matrix of eigenvectors, V, is:" << endl << es.eigenvectors() << endl << endl; 7 8 complex<double> lambda = es.eigenvalues()[0]; 9 cout << "Consider the first eigenvalue, lambda = " << lambda << endl; 10 VectorXcd v = es.eigenvectors().col(0); 11 cout << "If v is the corresponding eigenvector, then lambda * v = " << endl << lambda * v << endl; 12 cout << "... and A * v = " << endl << A.cast<complex<double> >() * v << endl << endl; 13 14 MatrixXcd D = es.eigenvalues().asDiagonal(); 15 MatrixXcd V = es.eigenvectors(); 16 cout << "Finally, V * D * V^(-1) = " << endl << V * D * V.inverse() << endl; 17