* change the nesting order of adjoint_return_type to

1 - make it easier to catch conjugate expressions
 2 - make sure there is no unecessary copy (we had NestByValue<Derived> which seems to be very bad)
* update eigensolver wrt recent changes

Eigen/src/Core/MatrixBase.h

@@ -258,8 +258,10 @@ template<typename Derived> class MatrixBase
     /** \internal the return type of MatrixBase::imag() */
     typedef CwiseUnaryView<ei_scalar_imag_op<Scalar>, Derived> NonConstImagReturnType;
     /** \internal the return type of MatrixBase::adjoint() */
-    typedef Eigen::Transpose<NestByValue<typename ei_cleantype<ConjugateReturnType>::type> >
-            AdjointReturnType;
+    typedef typename ei_meta_if<NumTraits<Scalar>::IsComplex,
+                        CwiseUnaryOp<ei_scalar_conjugate_op<Scalar>, NestByValue<Eigen::Transpose<Derived> > >,
+                        Transpose<Derived>
+                     >::ret AdjointReturnType;
     /** \internal the return type of MatrixBase::eigenvalues() */
     typedef Matrix<typename NumTraits<typename ei_traits<Derived>::Scalar>::Real, ei_traits<Derived>::ColsAtCompileTime, 1> EigenvaluesReturnType;
     /** \internal expression tyepe of a column */

Eigen/src/Core/Product.h

@@ -697,7 +697,8 @@ struct ei_cache_friendly_product_selector<ProductType,1,LhsOrder,LhsAccess,RhsCo
 {};
 
 
-/** \internal */
+/** \internal
+  * Overloaded to perform an efficient C += A*B */
 template<typename Derived>
 template<typename Lhs,typename Rhs>
 inline Derived&
@@ -710,7 +711,8 @@ MatrixBase<Derived>::operator+=(const Flagged<Product<Lhs,Rhs,CacheFriendlyProdu
   return derived();
 }
 
-/** \internal */
+/** \internal
+  * Overloaded to perform an efficient C -= A*B */
 template<typename Derived>
 template<typename Lhs,typename Rhs>
 inline Derived&
@@ -723,6 +725,8 @@ MatrixBase<Derived>::operator-=(const Flagged<Product<Lhs,Rhs,CacheFriendlyProdu
   return derived();
 }
 
+/** \internal
+  * Overloaded to perform an efficient C = A*B */
 template<typename Derived>
 template<typename Lhs, typename Rhs>
 inline Derived& MatrixBase<Derived>::lazyAssign(const Product<Lhs,Rhs,CacheFriendlyProduct>& product)

Eigen/src/Core/Transpose.h

@@ -181,7 +181,7 @@ template<typename Derived>
 inline const typename MatrixBase<Derived>::AdjointReturnType
 MatrixBase<Derived>::adjoint() const
 {
-  return conjugate().nestByValue();
+  return transpose().nestByValue();
 }
 
 /***************************************************************************