Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    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

    User Avatar
    2016 Award

    Staff: Mentor

    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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: What is *not* a Vector Function?
  1. What is a vector? (Replies: 2)

  2. What is a "function"? (Replies: 18)

Loading...