if u and v are objects in V, then u+v is in V
1
u+v = v+u
2
u+(v+w) = (u+v)+w
3
There is an object 0 in V called a zero vector for V,
Such that 0+u = u+0 = u
Such that 0+u = u+0 = u
4
For each u in V, there is an object -u in V, called a negative of u, such that u+(-u) = (-u)+u = 0
5
If k is any scalar and u is any object in V, then ku is in V.
6
k(u+v) = ku + kv
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(k+m)u = ku+mu
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k(mu) = (km)(u)
9
1u = u
10
