template<typename T, size_t n, size_t m>
class Matrix;

template<typename T, size_t n, size_t m>
class EtMatrixAdd
{
public:
  EtMatrixAdd(
  const Matrix<T, n, m>& lhs, 
  const Matrix<T, n, m>& rhs) : m_lhs(lhs), m_rhs(rhs) {}

  T ElementAt(size_t n, size_t m) const
  { return m_lhs.ElementAt(n, m) + m_rhs.ElementAt(n, m); }

private:
  const Matrix<T, n, m>& m_lhs;
  const Matrix<T, n, m>& m_rhs;
};

// In addition to operator= of Listing 1
template<typename T, size_t n, size_t m>
Matrix<T, n, m>& operator=(
  Matrix<T, n, m>& lhs, 
  const EtMatrixAdd<T, n, m>& rhs) {
  for(int i=0; i<n; ++i)
    for(int j=0; j<m; ++j)
      lhs.ElementAt(i,j) = rhs.ElementAt(i,j);
  return lhs;
}
  
// Replaces the operator+ of Listing 1
template<typename T, size_t n, size_t m>
inline EtMatrixAdd<T, n, m> operator+(
  const Matrix<T, n, m>& lhs, 
  const Matrix<T, n, m>& rhs) 
{ return EtMatrixAdd<T, n, m>(lhs, rhs); }