Linear Power Supply Advice
No, this won't work to give you +/- supplies, because of the common negative rail. 

You can, however, use the transformer you have to give you +/- adjustable supplies by using two half-wave rectifiers (2 diodes), double up on the capacitor values to keep the ripple at ~2Vp-p, and an LM317 for the positive and an LM337 for the negative supplies. With suitable (large) heat sinks capable of dissipating about 10W each it should be good for about +/-0.6A. You could also use 10,000uF caps (say 25V rated) to get a bit more voltage range at high current. 







simulate this circuit &ndash; Schematic created using CircuitLab