- Thread starter
- #1

- Jan 29, 2012

- 661

**jdm900712**

et V be a vector space over the field F. and TL(V, V) be a linear map.

Show that the following are equivalent:

a) Im TKer T = {0}

b) If T^2(v) = 0 -> T(v) = 0, vV

Using p -> (q -> r) <-> (pq) ->r

I suppose Im TKer T = {0} and T(v) = 0.

then I know that T(v)Ker T and T(v)Im T

so T(v) = 0.

I need help on how to prove the other direction.