Squashed 'third_party/eigen/' content from commit 61d72f6

Change-Id: Iccc90fa0b55ab44037f018046d2fcffd90d9d025
git-subtree-dir: third_party/eigen
git-subtree-split: 61d72f6383cfa842868c53e30e087b0258177257
diff --git a/doc/examples/tut_arithmetic_matrix_mul.cpp b/doc/examples/tut_arithmetic_matrix_mul.cpp
new file mode 100644
index 0000000..f213902
--- /dev/null
+++ b/doc/examples/tut_arithmetic_matrix_mul.cpp
@@ -0,0 +1,19 @@
+#include <iostream>
+#include <Eigen/Dense>
+
+using namespace Eigen;
+int main()
+{
+  Matrix2d mat;
+  mat << 1, 2,
+         3, 4;
+  Vector2d u(-1,1), v(2,0);
+  std::cout << "Here is mat*mat:\n" << mat*mat << std::endl;
+  std::cout << "Here is mat*u:\n" << mat*u << std::endl;
+  std::cout << "Here is u^T*mat:\n" << u.transpose()*mat << std::endl;
+  std::cout << "Here is u^T*v:\n" << u.transpose()*v << std::endl;
+  std::cout << "Here is u*v^T:\n" << u*v.transpose() << std::endl;
+  std::cout << "Let's multiply mat by itself" << std::endl;
+  mat = mat*mat;
+  std::cout << "Now mat is mat:\n" << mat << std::endl;
+}