---
# edu-hvmi
title: §4 What Is a Vector Database?
status: completed
type: task
priority: normal
created_at: 2026-03-10T23:30:02Z
updated_at: 2026-03-10T23:30:02Z
---

## §4 What Is a Vector Database? — Stub to fill

File: `edu/src/vector-db.md`, section `### 4. What Is a Vector Database?`

Replace this stub line with full content:
> A vector database is a data store built around one core operation [...] 🚧 Full content tracked in [nbd:d9f850].

This is a **reading lesson** — no Rust code. Target 500–700 words. Bold lead phrases.

## Learning objectives

- Understand the core operation: approximate nearest-neighbour (ANN) search
- Know the primary use cases that motivate vector databases
- Understand how vector databases differ from relational DBs and full-text search
- Know the key performance metrics: recall@k, QPS, index build time, memory

## Content to write

**The core operation.** Given a query vector q and n stored vectors, find the k vectors most similar to q. Exact KNN is O(n·d) per query — at n=1M and d=768 this means 768M operations per query, too slow for interactive use. Vector databases use ANN algorithms (see §5) that trade a small accuracy loss for orders-of-magnitude speed gains.

**Use cases.** Each described in one concrete sentence:
- Semantic search: find documents matching the *meaning* of a query, not just the words
- Recommendation: given an item, return the k most similar items (§11) or surface content preferred by similar users
- Retrieval-Augmented Generation (RAG): retrieve relevant passages before prompting an LLM, so the answer is grounded in facts (§12)
- Duplicate/near-duplicate detection: find items semantically identical or very close to a given item
- Anomaly detection: items far from all stored vectors are likely anomalous
- Multi-modal search: find images matching a text description, using CLIP-style joint embeddings

**vs. relational databases.** SQL WHERE clauses do exact matches and range queries on scalar values. There is no built-in notion of "nearest" for float arrays. Extensions like pgvector (PostgreSQL) and sqlite-vec (SQLite / Turso) add vector search to existing databases — this course uses sqlite-vec via the `libsql` crate.

**vs. full-text search (BM25/TF-IDF).** Keyword search cannot handle synonymy (car ≠ automobile without explicit expansion) or concept-level similarity. Vector search captures both. Hybrid search — combining BM25 and ANN scores — is a common production pattern that outperforms either alone.

**Key metrics.**
- Recall@k: fraction of the true k nearest neighbours that the ANN algorithm returns. A recall@10 of 0.95 means 95% of correct results are found.
- QPS: queries per second the index can serve at a given recall target.
- Index build time: one-time cost paid before serving queries.
- Memory footprint: HNSW stores graph edges in RAM; this limits how large the index can grow on a single machine.

**Where sqlite-vec / Turso fits.** sqlite-vec is appropriate for embedded applications, local development, and small-to-medium corpora (up to a few million vectors). Dedicated cloud vector databases (Pinecone, Qdrant, Weaviate) handle larger scale and add features like multi-tenancy, filtering, and distributed search.