Unit Vector
A vector with magnitude exactly 1, obtained by dividing by its own magnitude.
- Encodes pure direction, no scale.
- Cosine similarity on unit vectors = dot product.
- Standard basis e_1, e_2, ..., e_n are unit vectors.
When to use: Embedding retrieval, attention key normalization, geometric direction encoding.
Example: v = [3, 4], ||v|| = 5 → unit vector [0.6, 0.8]. OpenAI text-embedding-3 outputs unit-norm vectors.