Vector Space has a total of 8 Axioms, most of which are common-sense, but can still pose a challenge for memorizing by heart.
I created a mnemonic “MAD” which helps to remember them.
M for Multiplicative Axioms:
- (Scalar Multiplication identity)
- (Associativity of Scalar Multiplication)
A for Additive Axioms: (Note that these are precisely the axioms for an abelian group)
- (Associativity for Vector Addition)
- (Existence of Additive Inverse)
- (Additive Identity)
D for Distributive Axioms:
- (Distributivity of vector sums)
- (Distributivity of scalar sums)