I've a problem about kernel and endomorphism. And i'm a little bit worried 'cause i'm blocked when i've just answered the first question. But let's see...
Ok, so we have a -vector space and an endomophism of .
We have and .
So, i've prooved that we always have, for all ,
Now, the question is
Ok, now of course i've searche for a little while. But the fact is : i can't see how to start the proof. I think of several way : to prove it directly, maybe by induction, i've even think of trying it with contraposition !Show that, if , then
Well, so i really don't want the answer ! Please !
But just the smallest hint ( such as, the way to prove it ) which can make me see how to keep going.
Thanks for reading me ! And i apologize if my english is poor