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I What is *not* a Vector Function?

  1. Jun 22, 2016 #1
    i never thought of it before! every function that i've encountered has been a 'vector function' .. so what is not a vector function?
     
  2. jcsd
  3. Jun 22, 2016 #2

    mfb

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    2016 Award

    Staff: Mentor

    Depends on what exactly you call "vector function". If the codomain has to be a vector space, then simply take a set as codomain that cannot be interpreted as vector space:
    f:{1} -> {1,2,3,4,5,6}, f(1)=1.
     
  4. Jun 22, 2016 #3

    fresh_42

    Staff: Mentor

    But here ##f## is basically equal to the linear embedding of ##\{0\}## into the two-dimensional vector space ##\mathbb{Z}_3^2## :biggrin:
     
  5. Jun 22, 2016 #4

    mfb

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    That vector space has 9 elements, not 6. That number was carefully chosen.
     
  6. Jun 22, 2016 #5

    fresh_42

    Staff: Mentor

    Ooops ...
     
  7. Jun 25, 2016 #6
    there can be a covector function
    There are a lot of different tensors
     
    Last edited: Jun 25, 2016
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