Matrix4f A = MatrixXf::Random(4,4);
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cout << "Here is a random 4x4 matrix:" << endl << A << endl;
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HessenbergDecomposition<MatrixXf> hessOfA(A);
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MatrixXf H = hessOfA.matrixH();
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cout << "The Hessenberg matrix H is:" << endl << H << endl;
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MatrixXf Q = hessOfA.matrixQ();
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cout << "The orthogonal matrix Q is:" << endl << Q << endl;
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cout << "Q H Q^T is:" << endl << Q * H * Q.transpose() << endl;
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