# I What is *not* a Vector Function?

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1. Jun 22, 2016

### 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?

2. Jun 22, 2016

### 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.

3. Jun 22, 2016

### Staff: Mentor

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

4. Jun 22, 2016

### Staff: Mentor

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

5. Jun 22, 2016

### Staff: Mentor

Ooops ...

6. Jun 25, 2016

### wrobel

there can be a covector function
There are a lot of different tensors

Last edited: Jun 25, 2016