(C++) Matrix multiplication in a templated Matrix class

Question

I came across a problem with my matrix class and i can't find a solution.

Matrix = ROWSxCOLUMNS

Let A be a 3x4 matrix
Let B be a 4x5 matrix

The operation AxB (which is defined only if the columns of A match the rows of B) leads to a 3x5 matrix. I wanted to create a templated class that does just that.

Matrix<int,3,4> A;
Matrix<int,4,5> B;
Matrix<int,3,5> matrix = A*B;

My code:

    template <class T, unsigned int ROWS, unsigned int COLUMNS>
    class Matrix {
      public:

        /* blabla */

        const Matrix<T, ROWS, /* ? */ >&
          operator*(const Matrix<T, COLUMNS, /* ? */ >& matrix) const
        {
          /* multiplication */
        }

        /* blabla */
    };

I don't know what to insert in the /* ? */ sections. Is there a way to let the compiler accept any unsigned integer value? Should i rewrite the code in a different way?

Note: I'm creating this class for academic purposes, i don't care if there are already libraries that do this.

Answer 1

Use a template member function with an integer template parameter:

template<class T, unsigned int ROWS, unsigned int COLUMNS>
class Matrix {
public:
    ... 
    template<unsigned int N>
    Matrix<T, ROWS, N>
    operator*(const Matrix<T, COLUMNS, N>& matrix) const
    {
          /* multiplication */
    }
    ...
};

Also, do not return the value by reference.