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Linear Algebra / Linear Maps (Transformations)

  1. Dec 24, 2016 #1
    This isn't really a homework question, I just need help understanding the example:

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    So transformation takes complex n-tuple as input, and it seems output is also a complex n-tuple (which is what makes it "operator"). But permutations of n entries is not n. I'm confused! Let's use the simple example, let x = (1, 2, 3). Permutations of this vector would be a set of 3! entries:

    {(1, 2, 3),(1, 3, 2),(2, 1, 3),(2, 3, 1),(3, 1, 2),(3, 2, 1)}

    But the transformation seems to produce one single ordered n-tuple, rather than a whole set.

    Alternative interpretation would be that entries in the range of T: eta1, eta2, eta3, ..., etan are the number of permutations of the first n elements. But that also makes no sense, I would end up with a sequence of natural numbers that do not depend on the input vector.

    I must be misunderstanding something, and I have a feeling it's obvious. Any help would be appreciated, thanks in advance.

    (Note to moderator: I have not used the template since it is not applicable; no questions nor relevant equations. My thoughts and effort on the example have been included though. Also, apologies if I am posting in the wrong place.)
     
  2. jcsd
  3. Dec 24, 2016 #2

    FactChecker

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    That is not relevant to this problem. We are just talking about one particular permutation, π, not how many different ones there might be. Aπ is just one particular way of shuffling the elements of x.
     
  4. Dec 24, 2016 #3
    You are right! I was just about to post that I have figured it out. Thank you for your reply!
     
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