OpenGL feedback

I am a biologist and VERY new to computer graphics, so please forgive the vagueness of the question. I am interested in finding out more about the type of data that can be returned by the OpenGL feedback function. Does this function enable me to query the x’y’z’w’ values of a transformed vector resulting from a matrix multiplication, and can I use this output in other calculations without sending it further through the graphics pipeline? Are there other functions/extensions to allow this? Finally, does the Nvidia Linux driver for the GeForce (supposedly 100% OpenGL 1.2 compatable) support this feature ?
Thanks in advance for your help.