1MatrixXd X = MatrixXd::Random(5,5);
2MatrixXd A = X + X.transpose();
3cout << "Here is a random symmetric 5x5 matrix:" << endl << A << endl << endl;
4Tridiagonalization<MatrixXd> triOfA(A);
5MatrixXd Q = triOfA.matrixQ();
6cout << "The orthogonal matrix Q is:" << endl << Q << endl;
7MatrixXd T = triOfA.matrixT();
8cout << "The tridiagonal matrix T is:" << endl << T << endl << endl;
9cout << "Q * T * Q^T = " << endl << Q * T * Q.transpose() << endl;
10