It Works!
After sorting out some soldering mistakes and after debugging our Arduino code the prototype finally works.

One smaller problem we still have, is that the Arduino can’t give us as much power as we would need. But this can be solved easaly with an additional power supply.
For the moment the capacity of the matrix is still kind of limited. All it can to is light up LEDs whenever the infrared transistors get enough light. Any object that gets close enough to a transistor will trigger the accordant LED.
With some more programming we will be able to do much more.