ACIT4330-Page/content/Definitions/Vector Spaces/Properties of a Vector Space.md

• 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.