- #1
Fernando Revilla
Gold Member
MHB
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I quote an unsolved problem from MHF (Linear map problem) posted by user jdm900712
http://mathhelpforum.com/advanced-algebra/212908-linear-map-problem.htmlet V be a vector space over the field F. and TL(V, V) be a linear map.![]()
Show that the following are equivalent:
a) I am TKer T = {0}![]()
b) If T^2(v) = 0 -> T(v) = 0, vV![]()
Using p -> (q -> r) <-> (pq) ->r![]()
I suppose I am TKer T = {0} and T
(v) = 0.![]()
then I know that T(v)Ker T and T(v)
I am T![]()
so T(v) = 0.
I need help on how to prove the other direction.