MatrixXcf A = MatrixXcf::Random(4, 4);
HessenbergDecomposition<MatrixXcf> hd(4);
hd.compute(A);
cout << "The matrix H in the decomposition of A is:" << endl << hd.matrixH() << endl;
hd.compute(2 * A);  // re-use hd to compute and store decomposition of 2A
cout << "The matrix H in the decomposition of 2A is:" << endl << hd.matrixH() << endl;