Cosine Similarity

Definitions

Term Definition
Vector v = (v₁,…,vₙ)
Magnitude ‖v‖ = √(v₁² + v₂² + … + vₙ²)
Unit Vector (Direction) v̂ = v/‖v‖
Dot Product u·v = u₁v₁ + u₂v₂ + … + uₙvₙ
Cosine cos θ = (u·v)/(‖u‖·‖v‖)
Angle θ = arccos ((u·v)/(‖u‖·‖v‖))
Orthogonal u·v = 0 (θ = 90°)
Parallel v = αu with α > 0 (θ = 0°)
Anti-parallel v = βu with β < 0 (θ = 180°)