prove that Z(v,T)=Z(u,T) iff g(T)(u)=v, where g(t) is prime compared to a nullify -T of u. (which means f(t) is the minimal polynomial of u, i.e f(T)(u)=0). (i think that when they mean 'is prime compared to' that f(t)=ag(t) for some 'a' scalar).(adsbygoogle = window.adsbygoogle || []).push({});

i tried proving this way:

suppose, g(T)(u)=v and suppose v belongs to V v doesn't equal 0, so f(T)(u)=0=av

a=0, i need to show that some polynomial function of v belong to V too, but i don't really know how?

and i need help on other way proof (suppose, Z(v,T)=Z(u,T)).

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# Homework Help: Cyclic subspaces question.

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