* use transpose() instead of row vectors (more common use case)

* add a word about noalias and performance for BLAS users

doc/C02_TutorialMatrixArithmetic.dox

@@ -124,8 +124,14 @@ introducing a temporary here, so it will compile \c m=m*m as:
 tmp = m*m;
 m = tmp;
 \endcode
+If you know your matrix product can be safely evluated into the destination matrix without aliasing issue, then you can use the \c nolias() function to avoid the temporary, e.g.:
+\code
+c.noalias() += a * b;
+\endcode
 For more details on this topic, see \ref TopicEigenExpressionTemplates "this page".
 
+\b Note: for BLAS users worried about performance, expressions such as <tt>c.noalias() -= 2 * a.adjoint() * b;</tt> are fully optimized and trigger a single gemm-like function call.
+
 \section TutorialArithmeticDotAndCross Dot product and cross product
 
 The above-discussed \c operator* does not allow to compute dot and cross products. For that, you need the dot() and cross() methods.

doc/examples/tut_arithmetic_dot_cross.cpp

@@ -2,11 +2,14 @@
 #include <Eigen/Dense>
 
 using namespace Eigen;
+using namespace std;
 int main()
 {
   Vector3d v(1,2,3);
   Vector3d w(0,1,2);
 
-  std::cout << "Dot product: " << v.dot(w) << std::endl;
+  cout << "Dot product: " << v.dot(w) << endl;
-  std::cout << "Cross product:\n" << v.cross(w) << std::endl;
+  double dp = v.adjoint()*w; // automatic conversion of the inner product to a scalar
+  cout << "Dot product via a matrix product: " << dp << endl;
+  cout << "Cross product:\n" << v.cross(w) << endl;
 }

doc/examples/tut_arithmetic_matrix_mul.cpp

@@ -7,13 +7,13 @@ int main()
   Matrix2d mat;
   mat << 1, 2,
          3, 4;
-  Vector2d vec(-1,1);
+  Vector2d u(-1,1), v(2,0);
-  RowVector2d rowvec(2,0);
   std::cout << "Here is mat*mat:\n" << mat*mat << std::endl;
-  std::cout << "Here is mat*vec:\n" << mat*vec << std::endl;
+  std::cout << "Here is mat*u:\n" << mat*u << std::endl;
-  std::cout << "Here is rowvec*mat:\n" << rowvec*mat << std::endl;
+  std::cout << "Here is u^T*mat:\n" << u.transpose()*mat << std::endl;
-  std::cout << "Here is rowvec*vec:\n" << rowvec*vec << std::endl;
+  std::cout << "Here is u^T*v:\n" << u.transpose()*v << std::endl;
-  std::cout << "Here is vec*rowvec:\n" << vec*rowvec << 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;
 }