集合VがK上の線型空間:
commutativity:
∀x,y∈V(x+y=y+x)
associativity:
∀x,y,z∈V((x+y)+z=x+(y+z))
∀x∈V,∀α,β∈K((αβ)x=α(βx))
additive identity:
∃0∈V,∀v∈V(v+0=v)
0 is called the additive identity of V
additive inverse:
∀x∈V,∃xˉ∈V(x+xˉ=0)
xˉ is called the additive inverse of x∈V
multiplicative identity:
1x=x
distributive properties:
∀x,y∈V,∀α,β∈K
α(x+y)=αx+αy and (α+β)x=αx+βx
