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Math Help - Nilpotent operator once again.

  1. #1
    MHF Contributor Also sprach Zarathustra's Avatar
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    Nilpotent operator once again.

    Let T an S be nilpotent operators (both from V to V), and TS=ST.
    Prove:

    1. TS nilpotent
    2. T+S nilpotent


    Thank you all!
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  2. #2
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by Also sprach Zarathustra View Post
    Let T an S be nilpotent operators (both from V to V), and TS=ST.
    Prove:

    1. TS nilpotent
    2. T+S nilpotent


    Thank you all!
    Assume T^n=S^m=0.

    1. Then what is (TS)^{mn}? (You need to use that ST=TS.)

    2. Using the above result, what is (S+T)^{2mn}? To *see* what is going on, work out (S+T)^4, assuming S^2=T^2=0.
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