Multivector decomposition R·v·R†:
scalar:—
e₁:—
e₂:—
e₃:—
e₁e₂:—
e₁e₃:—
e₂e₃:—
e₁e₂e₃:—
Rotor: R = cos(θ/2) − sin(θ/2)·B̂
Rotation: v' = R·v·R†
Cl(3,0) basis:
1 scalar, 3 vectors, 3 bivectors, 1 pseudoscalar
Key identity:
e₁e₂e₁ = −e₂ (reflects e₂!)
|v|: —
|v'|: — (preserved!)
Rotation: v' = R·v·R†
Cl(3,0) basis:
1 scalar, 3 vectors, 3 bivectors, 1 pseudoscalar
Key identity:
e₁e₂e₁ = −e₂ (reflects e₂!)
|v|: —
|v'|: — (preserved!)