diff --git a/doc/snippets/HessenbergDecomposition_compute.cpp b/doc/snippets/HessenbergDecomposition_compute.cpp
new file mode 100644
index 0000000..50e3783
--- /dev/null
+++ b/doc/snippets/HessenbergDecomposition_compute.cpp
@@ -0,0 +1,6 @@
+MatrixXcf A = MatrixXcf::Random(4,4);
+HessenbergDecomposition<MatrixXcf> hd(4);
+hd.compute(A);
+cout << "The matrix H in the decomposition of A is:" << endl << hd.matrixH() << endl;
+hd.compute(2*A); // re-use hd to compute and store decomposition of 2A
+cout << "The matrix H in the decomposition of 2A is:" << endl << hd.matrixH() << endl;