+++
title = "§1 What Is a Vector?"
priority = 5
status = "todo"
ticket_type = "task"
dependencies = []
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## §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