Hello. I need confirmation on this: Let $\displaystyle T:V\rightarrow V$ be a linear operator on the (finite dimensional)vector sapce V. I know that when T is a proyector,ie,$\displaystyle T^2=T$, then the space is the direc sum of the Kernel of T and it's image,$\displaystyle V=ker(T)\oplus Im(T)$. Now it seems to me that this is also true for any operator($\displaystyle T^2\neq T$). am I correct?