Question Let $T:V\to V , dimV=n , \Bbb F= \Bbb C$ a linear map Prove that $KerT^n \oplus ImT^n=V$
Thoughts We tried using the rank nullity theorem but got stuck, as we don't know what is $dim(ImT+KerT)$
Question Let $T:V\to V , dimV=n , \Bbb F= \Bbb C$ a linear map Prove that $KerT^n \oplus ImT^n=V$
Thoughts We tried using the rank nullity theorem but got stuck, as we don't know what is $dim(ImT+KerT)$