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What symbol is used for linear operator actions?

  1. May 2, 2012 #1
    Given a vector v[itex]\in H[/itex]: R2->R3 which is a function from R2 to R3, and an operator G: H->H on the space H in which v lives, what is the most commonly used symbol to refer to this mapping, i.e., G(v)=G[itex]\otimes v[/itex] or something else?
     
  2. jcsd
  3. May 2, 2012 #2

    mathman

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    G(v) is fine.
     
  4. May 2, 2012 #3
    Thank you for replying, but I want to emphasize that G is a 3x3 matrix valued operator that multiplies the 3x1 vector valued function v then integrated over the entire domain, is the tensor product [itex]\otimes[/itex] appropriate? I used a dot but was complained about by the reviewer.
     
  5. May 2, 2012 #4
    The tensor product is not appropriate, neither is the dot. Using G(v) makes most sense. Is there a reason why you don't want to use G(v)?
     
  6. May 3, 2012 #5
    Thanks again for clarifying, I guess I just wanted to emphasize the matrix vector multiplication part, I'll use G(v) so that there's no ambiguity. One more question though, if I apply G n times to v, n>=0, is [itex]G^n(v)[/itex] appropriate?
     
  7. May 3, 2012 #6
    I found the notation G^n(v)=G(G(G...G(v)...)) in a textbook. Thank you both!
     
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