How to Remember the 8 Vector Space Axioms

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:

1. (Scalar Multiplication identity)
2. (Associativity of Scalar Multiplication)

A for Additive Axioms: (Note that these are precisely the axioms for an abelian group)

1. (Commutativity)
2. (Associativity for Vector Addition)
3. (Existence of Additive Inverse)
4. (Additive Identity)

D for Distributive Axioms:

1. (Distributivity of vector sums)
2. (Distributivity of scalar sums)

Author: mathtuition88

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