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976 B
+++ title = "§1 What Is a Vector?" priority = 5 status = "closed" ticket_type = "task" dependencies = [] +++
§1 What Is a Vector? — ALREADY COMPLETE
This section is fully written in edu/src/vector-db.md under ### 1. What Is a Vector?. No further content work is needed. Mark this ticket done.
What was written
- Definition: a vector is an ordered list of numbers; each element is a coordinate along one axis of a space
- Geometric intuition in 2D and 3D: magnitude (
‖v‖ = √(Σ vᵢ²)), direction, orthogonality via dot product - High-dimensional spaces: the curse of dimensionality, normalisation onto the unit hypersphere, dimensions are not individually interpretable features
- Vectors as representations: the key insight that similarity in meaning corresponds to proximity in vector space — the basis of everything that follows
- Notation used throughout the course: v,
v[i],‖v‖, d for dimension, n for number of stored vectors