diff --git a/src/OpenFOAM/matrices/Matrix/Matrix.C b/src/OpenFOAM/matrices/Matrix/Matrix.C
index de27a21058..7a59373716 100644
--- a/src/OpenFOAM/matrices/Matrix/Matrix.C
+++ b/src/OpenFOAM/matrices/Matrix/Matrix.C
@@ -33,21 +33,20 @@ License
 
 template<class Form, class Type>
 template<class ListType>
-Foam::tmp<Foam::Field<Type>> Foam::Matrix<Form, Type>::rightMultiplyImpl
+Foam::tmp<Foam::Field<Type>> Foam::Matrix<Form, Type>::AmulImpl
 (
-    const ListType& colVec
+    const ListType& x
 ) const
 {
     const Matrix<Form, Type>& mat = *this;
 
     #ifdef FULLDEBUG
-    if (mat.n() != colVec.size())
+    if (mat.n() != x.size())
     {
         FatalErrorInFunction
             << "Attempt to multiply incompatible Matrix and Vector:" << nl
             << "Matrix : (" << mat.m() << ", " << mat.n() << ')' << nl
-            << "Vector : " << colVec.size() << " rows" << nl
-            << "The number of Matrix columns must equal the Vector size" << nl
+            << "Matrix columns != Vector size (" << x.size() << ')' << nl
             << abort(FatalError);
     }
     #endif
@@ -59,7 +58,7 @@ Foam::tmp<Foam::Field<Type>> Foam::Matrix<Form, Type>::rightMultiplyImpl
     {
         for (label j = 0; j < mat.n(); ++j)
         {
-            result[i] += mat(i, j)*colVec[j];
+            result[i] += mat(i, j)*x[j];
         }
     }
 
@@ -69,21 +68,20 @@ Foam::tmp<Foam::Field<Type>> Foam::Matrix<Form, Type>::rightMultiplyImpl
 
 template<class Form, class Type>
 template<class ListType>
-Foam::tmp<Foam::Field<Type>> Foam::Matrix<Form, Type>::leftMultiplyImpl
+Foam::tmp<Foam::Field<Type>> Foam::Matrix<Form, Type>::TmulImpl
 (
-    const ListType& rowVec
+    const ListType& x
 ) const
 {
     const Matrix<Form, Type>& mat = *this;
 
     #ifdef FULLDEBUG
-    if (rowVec.size() != mat.m())
+    if (mat.m() != x.size())
     {
         FatalErrorInFunction
             << "Attempt to multiply incompatible Matrix and Vector:" << nl
             << "Matrix : (" << mat.m() << ", " << mat.n() << ')' << nl
-            << "Vector : " << rowVec.size() << " columns" << nl
-            << "The number of Matrix rows must equal the Vector size" << nl
+            << "Matrix rows != Vector size (" << x.size() << ')' << nl
             << abort(FatalError);
     }
     #endif
@@ -93,7 +91,7 @@ Foam::tmp<Foam::Field<Type>> Foam::Matrix<Form, Type>::leftMultiplyImpl
 
     for (label i = 0; i < mat.m(); ++i)
     {
-        const Type& val = rowVec[i];
+        const Type& val = x[i];
         for (label j = 0; j < mat.n(); ++j)
         {
             result[j] += val*mat(i, j);
diff --git a/src/OpenFOAM/matrices/Matrix/Matrix.H b/src/OpenFOAM/matrices/Matrix/Matrix.H
index 3ef51cbc84..9de6f4f3f0 100644
--- a/src/OpenFOAM/matrices/Matrix/Matrix.H
+++ b/src/OpenFOAM/matrices/Matrix/Matrix.H
@@ -85,13 +85,13 @@ class Matrix
         //- Allocate storage for the contents
         inline void doAlloc();
 
-        //- Multiply matrix with a column vector on the right (A * x)
+        //- Multiply matrix with vector (A * x)
         template<class ListType>
-        tmp<Field<Type>> rightMultiplyImpl(const ListType& colVec) const;
+        tmp<Field<Type>> AmulImpl(const ListType& x) const;
 
-        //- Multiply matrix with a row vector on the left (x * A)
+        //- Multiply matrix transpose with vector (AT * x, or x * A)
         template<class ListType>
-        tmp<Field<Type>> leftMultiplyImpl(const ListType& rowVec) const;
+        tmp<Field<Type>> TmulImpl(const ListType& x) const;
 
 
 public:
@@ -310,30 +310,27 @@ public:
         //- Return the transpose of the matrix
         Form T() const;
 
-        //- Multiply matrix with a column vector on the right (A * x)
-        inline tmp<Field<Type>> rightMultiply
+        //- Multiply matrix with vector (A * x)
+        inline tmp<Field<Type>> Amul
         (
-            const UList<Type>& colVec
+            const UList<Type>& x
         ) const;
 
-        //- Multiply matrix with a column vector on the right (A * x)
+        //- Multiply matrix with vector (A * x)
         template<class Addr>
-        inline tmp<Field<Type>> rightMultiply
+        inline tmp<Field<Type>> Amul
         (
-            const IndirectListBase<Type, Addr>& colVec
+            const IndirectListBase<Type, Addr>& x
         ) const;
 
-        //- Multiply matrix with a row vector on the left (x * A)
-        inline tmp<Field<Type>> leftMultiply
-        (
-            const UList<Type>& rowVec
-        ) const;
+        //- Multiply matrix transpose with vector (AT * x, or x * A)
+        inline tmp<Field<Type>> Tmul(const UList<Type>& x) const;
 
-        //- Multiply matrix with a row vector on the left (x * A)
+        //- Multiply matrix transpose with vector (AT * x, or x * A)
         template<class Addr>
-        inline tmp<Field<Type>> leftMultiply
+        inline tmp<Field<Type>> Tmul
         (
-            const IndirectListBase<Type, Addr>& rowVec
+            const IndirectListBase<Type, Addr>& x
         ) const;
 
 
diff --git a/src/OpenFOAM/matrices/Matrix/MatrixI.H b/src/OpenFOAM/matrices/Matrix/MatrixI.H
index 8abd40af82..a3edc704e6 100644
--- a/src/OpenFOAM/matrices/Matrix/MatrixI.H
+++ b/src/OpenFOAM/matrices/Matrix/MatrixI.H
@@ -404,44 +404,44 @@ void Foam::Matrix<Form, Type>::shallowResize(const label m, const label n)
 
 
 template<class Form, class Type>
-inline Foam::tmp<Foam::Field<Type>> Foam::Matrix<Form, Type>::rightMultiply
+inline Foam::tmp<Foam::Field<Type>> Foam::Matrix<Form, Type>::Amul
 (
-    const UList<Type>& colVec
+    const UList<Type>& x
 ) const
 {
-    return this->rightMultiplyImpl(colVec);
+    return this->AmulImpl(x);
 }
 
 
 template<class Form, class Type>
 template<class Addr>
-inline Foam::tmp<Foam::Field<Type>> Foam::Matrix<Form, Type>::rightMultiply
+inline Foam::tmp<Foam::Field<Type>> Foam::Matrix<Form, Type>::Amul
 (
-    const IndirectListBase<Type, Addr>& colVec
+    const IndirectListBase<Type, Addr>& x
 ) const
 {
-    return this->rightMultiplyImpl(colVec);
+    return this->AmulImpl(x);
 }
 
 
 template<class Form, class Type>
-inline Foam::tmp<Foam::Field<Type>> Foam::Matrix<Form, Type>::leftMultiply
+inline Foam::tmp<Foam::Field<Type>> Foam::Matrix<Form, Type>::Tmul
 (
-    const UList<Type>& rowVec
+    const UList<Type>& x
 ) const
 {
-    return this->leftMultiplyImpl(rowVec);
+    return this->TmulImpl(x);
 }
 
 
 template<class Form, class Type>
 template<class Addr>
-inline Foam::tmp<Foam::Field<Type>> Foam::Matrix<Form, Type>::leftMultiply
+inline Foam::tmp<Foam::Field<Type>> Foam::Matrix<Form, Type>::Tmul
 (
-    const IndirectListBase<Type, Addr>& rowVec
+    const IndirectListBase<Type, Addr>& x
 ) const
 {
-    return this->leftMultiplyImpl(rowVec);
+    return this->TmulImpl(x);
 }
 
 
@@ -546,7 +546,7 @@ inline Foam::tmp<Foam::Field<Type>> Foam::operator*
     const UList<Type>& x
 )
 {
-    mat.rightMultiply(x);
+    return mat.Amul(x);
 }
 
 
@@ -557,7 +557,7 @@ inline Foam::tmp<Foam::Field<Type>> Foam::operator*
     const IndirectListBase<Type, Addr>& x
 )
 {
-    mat.rightMultiply(x);
+    return mat.Amul(x);
 }
 
 
@@ -568,7 +568,7 @@ inline Foam::tmp<Foam::Field<Type>> Foam::operator*
     const Matrix<Form, Type>& mat
 )
 {
-    mat.leftMultiply(x);
+    return mat.Tmul(x);
 }
 
 
@@ -579,7 +579,7 @@ inline Foam::tmp<Foam::Field<Type>> Foam::operator*
     const Matrix<Form, Type>& mat
 )
 {
-    mat.leftMultiply(x);
+    return mat.Tmul(x);
 }