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Homework Help: Linear operator

  1. Oct 13, 2008 #1
    Can you help me with this, or at least give me an idea how to proceed:
    Let T:V->V be a linear operator on the vector space over the field F. Let v is in V and let m be a positive integer for which v is not equal to 0, T(v) is not equal to 0, ...,T^(m-1)(v) is not equal to 0, but T^m(v) is equal to 0. Show that {v, T(v), ... , T^(m-1)(v)} is linearly independent set.
    Thank you!
  2. jcsd
  3. Oct 14, 2008 #2
    Given [tex]a_0 v + a_1 T(v) + \cdots + a_{m-1} T^{m-1}(v) = 0[/tex], apply T to both sides repeatedly and see what you get.
    Last edited: Oct 14, 2008
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