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      1 MatrixXd X = MatrixXd::Random(5,5);
      2 MatrixXd A = X + X.transpose();
      3 cout << "Here is a random symmetric 5x5 matrix:" << endl << A << endl << endl;
      4 
      5 VectorXd diag(5);
      6 VectorXd subdiag(4);
      7 internal::tridiagonalization_inplace(A, diag, subdiag, true);
      8 cout << "The orthogonal matrix Q is:" << endl << A << endl;
      9 cout << "The diagonal of the tridiagonal matrix T is:" << endl << diag << endl;
     10 cout << "The subdiagonal of the tridiagonal matrix T is:" << endl << subdiag << endl;
     11