(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that the space of all shift maps is indeed a vector space over R and that there is a linear bijection between it and R2

2. Relevant equations

10 Axioms of vector spaces

Definition of bijection (1-1, onto)

For 1-1: f(a) = f(b) -> a = b.

3. The attempt at a solution

Ok ignoring the vector space proof for the moment my main problem was defining this space to begin with. I sorta saw it as the set of functions f st f(x) = x + a where x and a are sets or matrices of values from the field R. The only problem here is there is no limit really to the dimension of this space and so getting it to be a bijection to R2 could be a problem (here i assume that isomorphisms have the same dimension) or am i to limit our function space to dimension 2?

Im kinda muddeled on this one guys

Cheers

-G

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Vector space stuff

**Physics Forums | Science Articles, Homework Help, Discussion**