
#1
Apr2008, 02:37 PM

P: 4

If V is any vector space and S and T are linear operators on V such that ST=TS show that the null space and the range of T are invariant under S.
I think I need to begin by taking an element of the range of T and having S act on it and show that it stays in V? Can you help get me started? 



#2
Apr2008, 04:44 PM

P: 588

So say, t is an element in the range of T, what can you say about this element? 



#3
Apr2308, 06:53 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,904

If y is in the range of T, then there exist x such that T(x)= y. So S(T(x))= S(y). But that is equal to T(S(x)). So S(y) is in ? 


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