diff --git a/doc/examples/TutorialLinAlgComputeTwice.cpp b/doc/examples/TutorialLinAlgComputeTwice.cpp
new file mode 100644
index 0000000..06ba646
--- /dev/null
+++ b/doc/examples/TutorialLinAlgComputeTwice.cpp
@@ -0,0 +1,23 @@
+#include <iostream>
+#include <Eigen/Dense>
+
+using namespace std;
+using namespace Eigen;
+
+int main()
+{
+   Matrix2f A, b;
+   LLT<Matrix2f> llt;
+   A << 2, -1, -1, 3;
+   b << 1, 2, 3, 1;
+   cout << "Here is the matrix A:\n" << A << endl;
+   cout << "Here is the right hand side b:\n" << b << endl;
+   cout << "Computing LLT decomposition..." << endl;
+   llt.compute(A);
+   cout << "The solution is:\n" << llt.solve(b) << endl;
+   A(1,1)++;
+   cout << "The matrix A is now:\n" << A << endl;
+   cout << "Computing LLT decomposition..." << endl;
+   llt.compute(A);
+   cout << "The solution is now:\n" << llt.solve(b) << endl;
+}