What is *not* a Vector Function?

[nweissma]

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]

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]

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]

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

 

[fresh_42]

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

Ooops ...

 

[wrobel]

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