# What is *not* a Vector Function?

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

mfb
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.

fresh_42
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.
But here ##f## is basically equal to the linear embedding of ##\{0\}## into the two-dimensional vector space ##\mathbb{Z}_3^2##

mfb
Mentor
That vector space has 9 elements, not 6. That number was carefully chosen.

fresh_42
Mentor
That vector space has 9 elements, not 6. That number was carefully chosen.
Ooops ...

wrobel