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Jul 25, 2015 at 0:00 comment added Jason Starr @RaulGomez: "Is this extended map then surjective?" No, the extended map is not surjective. For instance, the element $(q^1,q^2,\dots,q^{n-1},q^n) = (0,0,\dots, 0,1)$ is not in the image.
Jul 24, 2015 at 23:11 comment added Raul Gomez I just have a small question regarding your answer. It seems to me that you should be able to extend the morphism $q$ that you are defining above to the whole of $\operatorname{End}_{k}(V)$. Is this extended map then surjective?
Jul 24, 2015 at 23:01 vote accept Raul Gomez
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Jul 24, 2015 at 3:21 history edited Jason Starr CC BY-SA 3.0
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S Jul 24, 2015 at 1:44 history answered Jason Starr CC BY-SA 3.0
S Jul 24, 2015 at 1:44 history made wiki Post Made Community Wiki by Jason Starr