I want to know, what exactly is the purpose of Yor Collective's Research Matrix?
It increases the research on your planets by 12 tp.
Since it's a one-per-planet building, does it provide like a percentage boost to other research buildings?
No, just the increase to research production.
Or, have I misunderstood its purpose? Because the description "... integrates research into planet's capital" (or something to that effect) is totally opaque for me...
That's understandable. Some of the descriptions can be quite unclear, if not outright contradictory.
Another question: Suppose I have a tile with 300% research bonus and another tile with 100% research bonus (plus of course a lot of tiles without bonus), where should I build the Research Matrix?
I'd build it on the 300% tile until I can replace it with something better, like the Invention Matrix.