Excerpted from Ma Advanced Mathematics

Number multiplication and addition are called vector, the result of the operation is still a vector, and the dimension has not changed.

It is not hard to see that addition satisfies the commutative, associative law:

  • Commutative law:
  • Associative law:

The product satisfies the commutative, associative, and distributive laws:

  • Commutative law:
  • Associative law:
  • The distributive law: