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Algebraic Properties of Vectors

• Commutative (vector) P + Q = Q + P

• Associative (vector) (P + Q) + R = P + (Q + R)

• Additive identity There is a vector 0 such
  that (P + 0) = P = (0 + P)
  for all P

• Additive inverse For any P there is a vector -P such that P + (-P) = 0

• Distributive (vector) r(P + Q) = rP + rQ

• Distributive (scalar) (r + s) P = rP + sP

• Associative (scalar) r(sP) = (rs)P

• Multiplicative identity For the real number 1,
  1P = P for each P

Geometric Transformations - 09 MAY 95

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