Undefined reference C++ with template class

I have this class:

matrix.h

#ifndef MATRIX_H
#define MATRIX_H
#include 
#include 

using namespace std;
template  class matrix;
template  ostream& operator<< (ostream& o, const matrix& m);

template 
class matrix
{
    public:
        matrix(const int&);
        void push(const T&);
        void setRows(const int&);
        int size();
        T& operator ()(const int&, const int&);
        friend ostream& operator<< <>(ostream&, const matrix&);
        virtual ~matrix();
    private:
        vector elements_;
        int dimension_;
};

#endif // MATRIX_H

#include "matrix.h"
#include 

matrix.cpp

template 
matrix::matrix(const int& n)
{
    dimension_ = n;
}

template 
void matrix::push(const T& element)
{
    elements_.resize( elements_.size() + 1, element);
}

template 
int matrix::size()
{
    return elements_.size()/dimension_;
}

template 
T& matrix::operator ()(const int &n, const int &m)
{
    if ((n < 0) || (n > dimension_))
    {
        cerr << "Row index out of range"
             << endl << endl;
    }
    if ((m < 0) || (m > dimension_))
    {
        cerr << "Column index out of range"
             << endl << endl;
    }

    return elements_[n*dimension_+m];
}

template 
ostream& operator << (ostream& o, const matrix& m)
{
    for (int i = 0; i < m.size(); i++)
    {
        for (int j = 0; j < m.size(); i++)
        {
            o << m(i,j) << " ";
        }
        o << endl;
    }
    return o;
}


template 
matrix::~matrix()
{
    //dtor
}

And this program:

#include "matrix.h"
#include 

using namespace std;

int main()
{
    matrix m(3);
    m.push(10);
    m.push(10);
    m.push(11);
    m.push(11);
    m.push(12);
    m.push(12);
    m.push(13);
    m.push(13);
    m.push(10);
    cout << m;
    cout << "Hello world!" << endl;
    return 0;
}

And for EACH. SINGLE. ONE. Of the methods I call, I get a compiler error like this one:

C:\Users...\main.cpp|8|undefined reference to
`matrix::matrix(int const&)'|

I have the matrix.cpp file built. I'm using Code::Blocks, so I have a matrix.o file in the obj folder. That's not the problem.

What is it?