I could really do with some help. I'm trying to show that the face of a face of a convex polyhedral cone is again a face of that polyhedral cone. I have spent a couple hours thinking about this and CAN'T show it. The following apparently gives a proof of this, but it's surely invalid http://img30.imageshack.us/img30/4752/vsqc.png [Broken] The bit I have underlined. I can see literally no reason why [itex] \langle u, v \rangle \geq 0[/itex] would mean that [itex] \langle u, v \rangle = 0[/itex]. Can anyone help?