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Linear Algebra Axiom

The ten axioms for vector spaces

Axiom NumberAxiom
Axiom 01 If u and v are objects in V, then u + v is in V
Axiom 02 u + v = v + u
Axiom 03 u + (v + w) = (u + v) + w
Axiom 04 There is an object 0 in V, called a "zero vector" for V, such that 0 + u = u + 0 = u for all u in V
Axiom 05 For each u in V, there is an object -u in V, called a "negative" of u, such that u + (-u) = (-u) + u = 0
Axiom 06 If k is any scalar and u is any object in V, then ku is in V
Axiom 07 k(u + v) = ku + kv
Axiom 08 (k + m)u = ku + mu
Axiom 09 k(mu) = (km)u
Axiom 10 1u = u
Created by: Ultric