Why I cannot define friend of template outside the class?

Question

I am reading about STL containers so when I got to the relational operators how work with them: I found that the containers use the Element Type Relational Operator when two containers of the same type are compared, How ever I'd like to break their rule and define a relational operator that doesn't depend on the operation provided by the element type.

#include <iostream>



template<class T>
class Vector {
    public:
        using size_type = unsigned int;

        Vector() = default;
        Vector(size_type, T = T());

        size_type size()const { return sz_; }
        T* elem()const { return elem_; }

        ~Vector();

        friend bool operator < (const Vector<T>& x, const Vector<T>& y);

    private:
        T* elem_ = nullptr;
        size_type sz_ = 0;
};

template<class T>
Vector<T>::Vector(size_type sz, T x) :
    sz_(sz ? sz : 0),
    elem_(sz ? new T[sz] : nullptr) {
    for (size_type i{}; i != sz_; ++i)
        elem_[i] = x;
}

template<class T>
Vector<T>::~Vector() {
    delete[] elem_;
    sz_ = 0;
}


template<class T>
bool operator < (const Vector<T>& x, const Vector<T>& y) {
    return x.sz_ < y.sz_;
}


class A{
    public:

};



int main(){

    Vector<int> v1(7);
    Vector<int> v2(9);

    std::cout << (v1 < v2) << std::endl;

    Vector<A> v3(10);
    Vector<A> v4(12);

    std::cout << (v3 < v4) << std::endl;

}

But When I compile the program runs fine but if I define the < it doesn't work so I get link-time error complaining about the definition of:

/usr/bin/ld: /home/5jxZPM/prog-a06418.o: in functionmain': prog.cpp:(.text+0x5e): undefined reference to operator<(Vector<int> const&, Vector<int> const&)'

• If I define it inside the class then it works fine!

  template<class T>
  class Vector {
      public:
          friend bool operator < (const Vector<T>& x, const Vector<T>& y){
              return x.sz_ < y.sz_;
          }
      //...
  };