Find a linear map T from R^2 to R^2 such that T is neither 0 nor the identity map, but T^2 = T. (Any help would be appreciated).

Question

anonymous · Answer

You should try http://math.stackexchange.com/ if we're unable to help.

turingtest · Answer

$$T^2=T\implies TT=T\implies T=T^{-1}T=I$$but you want something besides the identity transformation
I feel like I just proved that's impossible...

anonymous · Answer

I'm not sure if there exists any other $\{T=T^2\mid T\notin\emptyset,I\}$.

anonymous · Answer

I've asked on math.stackexchange. Of course, I'll repay the help I get there with mathematics I understand a bit more (statistics and probability I). Thanks!