Question

Is it possible to overload operator +

template <typename U>
Mat <T> operator + ( const Mat <U> &A );

for the following matrix operations

Matrix (1,1) + scalar      = scalar
scalar + Matrix (1,1)      = scalar
Matrix(1,1) + Matrix(1,1)  = scalar

and a syntax (or alike)?

template <typename T, typename U>
T operator + ( const Mat <U> &M ) const;

Updated question:

The dimension as a template parameter:

template <typename T, typename U, const unsigned int TDim>
T operator + ( const Mat <U> &M, TDim <dim> ) const;

with the specialization for dim=1

template <typename T, typename U>
T operator + ( const Mat <U> &M, TDim <1> ) const;

Answer 1

Not unless the dimensions of the matrix are made into template parameters of Mat, and you partially specialize the Mat template for 1x1 matrices.

Alternatively, you could return Matrix(1,1) and then have a conversion to scalar. If you did this, you’d have to accept the possibility of the conversion failing at runtime.