Math1231 Vector Axioms

Any set that holds true for these ten laws is considered a vector space.

1. Closure under addition

2. Associative law of addition

3. Commutative addition law

4. Existence of a zero (u + 0 = 0)

5. Existence of a negative (u + w = 0, therefore w = -u)

6. Closure under scalar multiplication

7. Associative law of scalar multiplication

8. Existence of a one (1 * u = u)

9. Scalar distributive law

10. Vector distributive law