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Math Help - nilpotent

  1. #1
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    nilpotent

    I have a question on an assignment that says: Suppose that T,S ∈ L(V). Show that ST is nilpotent if and only if TS is nilpotent.

    All I can figure is this but it almost seems to easy

    If ST is nilpotent, then ∃n ∈ N such that (ST)n = 0, so (TS)n+1 = T(ST)nS = 0

    Any comments are appreciated!
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  2. #2
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    Quote Originally Posted by falloutboy10 View Post
    I have a question on an assignment that says: Suppose that T,S ∈ L(V). Show that ST is nilpotent if and only if TS is nilpotent.

    All I can figure is this but it almost seems to easy

    If ST is nilpotent, then ∃n ∈ N such that (ST)n = 0, so (TS)n+1 = T(ST)nS = 0

    Any comments are appreciated!


    Yes, it's that easy...

    Tonio
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