Properties of a Vector Space

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

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