I always thought a "Prime" drew their power from the Allspark via the Matrix.

When Optimus Primal took the 'Matrix-shaped' object from Prime's chest in Optimal Situation, I believed he was taking the 'actual' Matrix into his body, as a Prime's spark is in essense already one with the Allspark inside the Matrix.

So basically, The Matrix is a Prime's Spark that is empowered by the Allspark and is housed in the double-handled canister we know and love.