- #1
pjallen58
- 12
- 0
I am trying to shorten and generalize the the definition of a vector space to redefine it in such a way that only four axioms are required. The axioms must hold for all vectors u, v and w are in V and all scalars c and d.
I believe the four would be:
1. u + v is in V,
2. u + 0 = u
3. u + -u = 0
4. cu is in V
I believe 1 and 2 can be used to satisfy:
u + v = v + u
(u + v) + w = u + (v + w)
and 3 and 4 can be used to satisfy:
c(u + v) = cu + cv
(c + d)u = cu + du
c(du) = (cd)u
1u = u
Not sure if I am on the right track here so any suggestions or corrections would be appreciated. Thanks to all who reply.
I believe the four would be:
1. u + v is in V,
2. u + 0 = u
3. u + -u = 0
4. cu is in V
I believe 1 and 2 can be used to satisfy:
u + v = v + u
(u + v) + w = u + (v + w)
and 3 and 4 can be used to satisfy:
c(u + v) = cu + cv
(c + d)u = cu + du
c(du) = (cd)u
1u = u
Not sure if I am on the right track here so any suggestions or corrections would be appreciated. Thanks to all who reply.