Befriending a function template defined in another file in C++11?

I have written a custom vector class template and print_vector function template that is supposed to print the content of my custom vector class. The print_vector function uses v.sz and v.elem which are declared private inside the vector class. However I am unable to declare print_vector as a friend inside my vector class. I want to keep the print_vector separately defined in t_vector.cpp.

A problem is that print_vector takes a parameter of the same type as the class it is declared friend in (becomes a circular dependency?). I also get an error saying that print_vector is not declared in scope.

I have marked the problematic places with // <--

// t_vector.h
#ifndef T_VECTOR_H
#define T_VECTOR_H

#include <string>

template <typename T>
void print_vector(Vector<T>& v);

template <typename T>
struct Vector {
private:
    int sz;
    T* elem;

public:
    Vector() = delete;

    explicit Vector(int s);

    Vector(const Vector<T>& v); 

    ~Vector(); 

    Vector<T>& operator=(const Vector<T>& v); 

    T& operator[](int e) const;

    template<typename U>
    friend void print_vector(Vector<U>& v); // <-- TRYING TO FRIEND print_vector
};
#endif

// t_vector.cpp
#include "t_vector.h"

#include <stdexcept>
#include <iostream>
#include <string>
using std::cout;
using std::endl;
using std::string;

template <typename T>
Vector<T>::Vector(int s) {
    if (s < 0) throw std::invalid_argument("Negative size");
    cout << this << " called Vector(int s) constructor" << endl;
    sz = s;
    elem = new T[sz];
}

template <typename T>
Vector<T>::Vector(const Vector<T>& v) : sz{v.sz}, elem{new T[v.sz]} { 
    cout << this << " called Copy constructor on " << &v << endl;
    for (int i = 0; i<sz; ++i) {
        elem[i] = v[i];
    }
}

template <typename T>
Vector<T>::~Vector() {
    cout << "~" << this << " delete elem " << &elem << endl;
    delete[] elem;
}

template <typename T>
Vector<T>& Vector<T>::operator=(const Vector<T>& v) {
    cout << this << " called Copy assignment operator to copy " << &v << endl;
    if (this != &v) {
        T *tmp = new T[v.sz];
        for (int i=0; i<v.sz; ++i ) {
            tmp[i] = v.elem[i];
        }
        sz = v.sz; 
        delete[] elem;
        elem = tmp;
    }
    return *this;
}

template <typename T>
T& Vector<T>::operator[](int e) const {
    if (e < 0 || e >= sz) throw std::out_of_range("Vector::operator[]"); 
    return elem[e];
}

template <typename T>
void print_vector(Vector<T>& v) { // <--- THIS FUNCTION WANTS TO READ v.sz WHICH IS PRIVATE
    for (int i = 0; i < v.sz-1; ++i) {
        cout << '[' << v.elem[i] << ']';
    }
    cout << '[' << v[v.sz-1] << ']' << endl;
}

// test_t_vector.cpp
#include "t_vector.h"
#include "t_vector.cpp" 

#include <iostream>
using std::cout;
using std::endl;

int main() {
    cout << "---------- Starting: test_vector ----------" << endl;

    Vector<int> vec(3);
    
    vec[2] = 5;
    print_vector(vec);

    cout << "---------- Exiting: test_vector ----------" << endl;
    return 0; 
}

Error output:

g++ -O0 -Wall -Wextra -pedantic-errors -Wold-style-cast  -fno-elide-constructors  -std=c++14  -g -ggdb3  -MT t_vector.o -MMD -MP -MF t_vector.d -std=c++14 -I.  -c -o t_vector.o t_vector.cpp
In file included from t_vector.cpp:1:
t_vector.h:7:6: error: variable or field ‘print_vector’ declared void
    7 | void print_vector(Vector<T>& v);
      |      ^~~~~~~~~~~~
t_vector.h:7:19: error: ‘Vector’ was not declared in this scope
    7 | void print_vector(Vector<T>& v);
      |                   ^~~~~~
t_vector.h:7:27: error: expected primary-expression before ‘>’ token
    7 | void print_vector(Vector<T>& v);
      |                           ^
t_vector.h:7:30: error: ‘v’ was not declared in this scope
    7 | void print_vector(Vector<T>& v);
      |                              ^
make: *** [<builtin>: t_vector.o] Error 1

As Ted Lyngmo and Retired Ninja mentioned the problem is that the implementation should have been visible in the header file. One of the methods to achieve this is to include a .tpp file with all the template implementations in the header file and include this file in the end of the header file. Unfortunately my class template seemed to work despite separating the class template declaration in the header file and the implementation details in a cpp file. This can occur by luck but the general rule is to show implementation details in header one way or another.