^^GA geometric algebra. Appunti.

a = a₁e₁ + a₂e₂ ;   e₁ e₂ base ortonormale.

We look for product of vectors

• associative, distributive. such that
• vector squares to the square of its magnitude: a² = |a|² = a₁² + a₂².

Quali conseguenze?

a² = (a₁e₁ + a₂e₂)(a₁e₁ + a₂e₂)

     =  a₁² + a₂² + a₁a₂(e₁e₂ + e₂e₁)
 

(1)

e₁e₂ + e₂e₁ = 0

e₁e₂ = -e₂e₁

(2)

(e₁e₂)² = (e₁e₂)(e₁e₂) = e₁(e₂e₁)e₂ = e₁(-e₁e₂)e₂ = -e₁²e₂² = -1