内積1

z=ab
z=e^iθ
e^iθ=cosθ+isinθ
z=cosθ+isinθ
z=abe^iθ
z=abcosθ
θ=0
θ=2π
z=ab
θ=π
z=-ab

(-ab)≦a•b≦ab
ab/(-ab)=r
ab/(-ab)=1/(-1)=r
ab/(-ab)=1/(-1)=-1=r
r=-1
An=r^(n-1)A1
An+1=(r^n)A1
An=A1[r^(n-1)]
An+1=A1[(r^n)]
An+1=rAn
An+1/An=r
An+1=rAn
rAn=An+1
r=An+1/An
rAn=An+1
An+1=rAn
r=-1
An+1=(-1)An
(-1)An+1=An
An=(-1)An+1
A=ab
(ab)n=(-1)(ab)n+1
(ab)n=(-ab)n+1
(-ab)≦a•b≦ab
a•b≦ab
ab≧a•b
a^2b^2≧(a•b)^2
a=Δa
b=Δb
(Δa)^2(Δb)^2≧(Δa•Δb)^2
Δa•Δb=1/2(Δa•Δb)+1/2(Δa•Δb)
Δa•Δb=1/2(Δa•Δb)+1/2(Δa•Δb)+1/2(Δa•Δb)-1/2(Δa•Δb)
Δa•Δb=1/2(Δa•Δb)+1/2(Δb•Δa)+1/2(Δa•Δb)-1/2(Δb•Δa)
Δa•Δb=1/2[(Δa•Δb)+(Δb•Δa)]+1/2[(Δa•Δb)-(Δb•Δa)]
Δa•Δb=1/2[(Δa•Δb)+(Δb•Δa)+(Δa•Δb)-(Δb•Δa)]

取り扱い説明書

(-ab)≦a•b≦abは内積