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      1 MatrixXcf A = MatrixXcf::Random(4,4);
      2 HessenbergDecomposition<MatrixXcf> hd(4);
      3 hd.compute(A);
      4 cout << "The matrix H in the decomposition of A is:" << endl << hd.matrixH() << endl;
      5 hd.compute(2*A); // re-use hd to compute and store decomposition of 2A
      6 cout << "The matrix H in the decomposition of 2A is:" << endl << hd.matrixH() << endl;
      7