diff --git a/Eigen/src/Cholesky/LLT.h b/Eigen/src/Cholesky/LLT.h
index 53e97cd3f..4527067a8 100644
--- a/Eigen/src/Cholesky/LLT.h
+++ b/Eigen/src/Cholesky/LLT.h
@@ -116,7 +116,7 @@ template<typename MatrixType, int _UpLo> class LLT
     bool m_isInitialized;
 };
 
-template<typename MatrixType/*, int UpLo*/>
+template<typename MatrixType>
 bool ei_inplace_llt_lo(MatrixType& mat)
 {
   typedef typename MatrixType::Scalar Scalar;
@@ -157,7 +157,7 @@ bool ei_inplace_llt_lo(MatrixType& mat)
   return true;
 }
 
-template<typename MatrixType/*, int UpLo*/>
+template<typename MatrixType>
 bool ei_inplace_llt_up(MatrixType& mat)
 {
   typedef typename MatrixType::Scalar Scalar;
diff --git a/Eigen/src/Core/MatrixBase.h b/Eigen/src/Core/MatrixBase.h
index 309661f67..cfa41978e 100644
--- a/Eigen/src/Core/MatrixBase.h
+++ b/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 */
diff --git a/Eigen/src/Core/Product.h b/Eigen/src/Core/Product.h
index 39b211fa1..0652eb615 100644
--- a/Eigen/src/Core/Product.h
+++ b/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)
diff --git a/Eigen/src/Core/Transpose.h b/Eigen/src/Core/Transpose.h
index c5e52d1dd..65127d175 100644
--- a/Eigen/src/Core/Transpose.h
+++ b/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();
 }
 
 /***************************************************************************
diff --git a/Eigen/src/QR/SelfAdjointEigenSolver.h b/Eigen/src/QR/SelfAdjointEigenSolver.h
index 70984efab..ff6b98aa1 100644
--- a/Eigen/src/QR/SelfAdjointEigenSolver.h
+++ b/Eigen/src/QR/SelfAdjointEigenSolver.h
@@ -259,11 +259,11 @@ compute(const MatrixType& matA, const MatrixType& matB, bool computeEigenvectors
 
   // compute C = inv(L) A inv(L')
   MatrixType matC = matA;
-  cholB.matrixL().solveTriangularInPlace(matC);
+  cholB.matrixL().solveInPlace(matC);
   // FIXME since we currently do not support A * inv(L'), let's do (inv(L) A')' :
-  matC = matC.adjoint().eval();
-  cholB.matrixL().template marked<LowerTriangular>().solveTriangularInPlace(matC);
-  matC = matC.adjoint().eval();
+  matC.adjointInPlace();
+  cholB.matrixL().solveInPlace(matC);
+  matC.adjointInPlace();
   // this version works too:
 //   matC = matC.transpose();
 //   cholB.matrixL().conjugate().template marked<LowerTriangular>().solveTriangularInPlace(matC);
@@ -277,7 +277,7 @@ compute(const MatrixType& matA, const MatrixType& matB, bool computeEigenvectors
   if (computeEigenvectors)
   {
     // transform back the eigen vectors: evecs = inv(U) * evecs
-    cholB.matrixL().adjoint().template marked<UpperTriangular>().solveTriangularInPlace(m_eivec);
+    cholB.matrixU().solveInPlace(m_eivec);
     for (int i=0; i<m_eivec.cols(); ++i)
       m_eivec.col(i) = m_eivec.col(i).normalized();
   }