What is *not* a Vector Function?

  • #1
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i never thought of it before! every function that i've encountered has been a 'vector function' .. so what is not a vector function?
 

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  • #2
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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.
 
  • #3
fresh_42
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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.
But here ##f## is basically equal to the linear embedding of ##\{0\}## into the two-dimensional vector space ##\mathbb{Z}_3^2## :biggrin:
 
  • #4
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That vector space has 9 elements, not 6. That number was carefully chosen.
 
  • #6
wrobel
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i never thought of it before! every function that i've encountered has been a 'vector function' .. so what is not a vector function?
there can be a covector function
There are a lot of different tensors
 
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