c++ - Can't understand why XCode linker doesn't see certain methods

I've just picked up C++ after years of meaning to. Right now I'm trying to implement a simple matrix class to be used from other classes. Following GManNickG's lead, here's my SimpleMatrix (declared in "SimpleMatrix.h"):

#pragma once
#include 


template 
class SimpleMatrix {    
    unsigned int numCols, numRows;    
public:    
    std::vector data;

    SimpleMatrix(unsigned int cols, unsigned int rows) :
    numCols(cols),
    numRows(rows),

    data(numCols * numRows)
    {};

    T getElement(unsigned int column, unsigned int row);
    void setShape(unsigned int column, unsigned int row, const T& initValue);    
};

and implemented as (in "SimpleMatrix.cpp"):

#include "SimpleMatrix.h"

template 
T SimpleMatrix::getElement(unsigned int column, unsigned int row) {   
    return data[row * numCols - 1];    
}

template 
void SimpleMatrix::setShape(unsigned int columns, unsigned int rows, const T& initValue) {
    numCols = columns;

    numRows = rows;
    data.assign(columns * rows, initValue);
}

Now, when I use SimpleMatrix from main, it compiles, links and works fine. When I try to use it from an object Container declared as (in "Container.h"):

#include "SimpleMatrix.h"

class Container {

public:    
    SimpleMatrix matrix;    
    Container();    
    void doStuff();
};

and implemented as (in "Container.cpp"):

#include "Container.h"

#include "SimpleMatrix.h"

void Container::doStuff() {    
    this->matrix.setShape(2, 2, 0);
    this->matrix.getElement(1, 1);
}

Xcode complains that

Undefined symbols for architecture x86_64:

"SimpleMatrix::getElement(unsigned int, unsigned int)", referenced from:
Container::doStuff() in Container.o   

"SimpleMatrix::setShape(unsigned int, unsigned int, int const&)", referenced from:
Container::doStuff() in Container.o 

ld: symbol(s) not found for architecture x86_64 clang: error: linker command failed with exit code 1 (use -v to see invocation)

I've checked the "Build Phases/Compile Sources"-settings, and all three files are there (main.cpp, SimpleMatrix.cpp, and Container.cpp).

There are probably a number of issues with this code. One that springs to mind is the lack of a default constructor for SimpleMatrix, but that's not really what concerns me here. I just can't understand what the fundamental difference between the two cases is.

Any help is greatly appreciated.

Answer

Implementation of templates has to be in the header file.