- $u + v = v + u$,
- $(u+v) + w = u + (v + w)$,
- $u + 0 = u$,
- $u + (-u) = 0$,
- $a (u + v) = a \times u + a \times v$,
- $(a + b) \times v = av + bv$,
- $a(bv) = (ab) \times v$,
- $1 \times v = v$.

These can be used for Complex, Real, or Rational vector spaces.