How to properly overload the << operator for an ostream?

Just telling you about one other possibility: I like using friend definitions for that:

namespace Math
{
    class Matrix
    {
    public:

        [...]

        friend std::ostream& operator<< (std::ostream& stream, const Matrix& matrix) {
            [...]
        }
    };
}

The function will be automatically targeted into the surrounding namespace Math (even though its definition appears within the scope of that class) but will not be visible unless you call operator<< with a Matrix object which will make argument dependent lookup find that operator definition. That can sometimes help with ambiguous calls, since it's invisible for argument types other than Matrix. When writing its definition, you can also refer directly to names defined in Matrix and to Matrix itself, without qualifying the name with some possibly long prefix and providing template parameters like Math::Matrix<TypeA, N>.

You have declared your function as friend. It's not a member of the class. You should remove Matrix:: from the implementation. friend means that the specified function (which is not a member of the class) can access private member variables. The way you implemented the function is like an instance method for Matrix class which is wrong.

To add to Mehrdad answer ,

namespace Math
{
    class Matrix
    {
       public:

       [...]


    }   
    std::ostream& operator<< (std::ostream& stream, const Math::Matrix& matrix);
}

In your implementation

std::ostream& operator<<(std::ostream& stream, 
                     const Math::Matrix& matrix) {
    matrix.print(stream); //assuming you define print for matrix 
    return stream;
 }