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      1 MatrixXd A(3,3);
      2 A << 4,-1,2, -1,6,0, 2,0,5;
      3 cout << "The matrix A is" << endl << A << endl;
      4 
      5 LLT<MatrixXd> lltOfA(A); // compute the Cholesky decomposition of A
      6 MatrixXd L = lltOfA.matrixL(); // retrieve factor L  in the decomposition
      7 // The previous two lines can also be written as "L = A.llt().matrixL()"
      8 
      9 cout << "The Cholesky factor L is" << endl << L << endl;
     10 cout << "To check this, let us compute L * L.transpose()" << endl;
     11 cout << L * L.transpose() << endl;
     12 cout << "This should equal the matrix A" << endl;
     13