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Prove if T is a Tensor

  1. Sep 20, 2010 #1
    A tensor T operates on a vector a and gives:

    Ta=a/(magnitude)a

    Is this a tensor?

    given previous examples of such questions I know that if Ta=3a then T(a+b)=3(a+b)=3a+3b. So I have an idea of how to solve these

    Well by looking at what I have if I substituted just like the examples I come up with

    T(a+b)=(a+b)/(magnitude) (a+b)

    Given this I belive that it isn't a tensor, but should I solve further for the magnitude which will be the square root of vector "a+b". Somehow I am not certain though, should I set T(b) equal to an equation? I am just confused please help
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 20, 2010 #2

    HallsofIvy

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    Well, what definition of "tensor" are you using? And what would Ta be if the magnitude of a were 0?
     
  4. Sep 20, 2010 #3
    A tensor transforms a vector into another vector, just like a
    dyad. T assigns to an arbitrary vector a to another vector, denoted by Ta and it must satisfy T(au + bv) = aTu + bTv

    I believe it would also be for all values other than zero
     
  5. Sep 20, 2010 #4

    HallsofIvy

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    So far, you have just said that a tensor is a linear transformation- and not all linear transformations are tensors. The crucial point is in that phrase "just like a dyad". What does that mean?
     
  6. Sep 20, 2010 #5
    HI, dear all,

    I am very sorry to post my question here since I cannot find where to start a new thread ...sorry ..

    Currently I am reading the paper "spatial scan statistics: approximation and performance study " and confused with section 4.1. I read many times , but still cannot get the meaning how the formula of (4.2) come from and why hi=p /4 can give a very good approximation for the convex function? could you guide me which mathematic theoretic background I should read or...how to understand this part? Futhermore, in fact,I cannot relate lemma 4.2 to the part of explaination using Figure 3 (a),(b).

    This paper --spatial scan statistics: approximation and performance study (authors: Deepal Agarwal, Andrew McGregor, etc.) , can be downloaded on website from google searching....


    Hope can helpe me to figure out !

    thanks !
    linsey
     
  7. Sep 20, 2010 #6

    HallsofIvy

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    There is a "New Topic" button just below the title of each category.
     
  8. Sep 20, 2010 #7
    I GOT IT! I was looking in way to deep into this equation. In a way you check if it is linear and substitute in another variable. Very easy! Thanks for your help!
     
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