Why it matters

Vector DB math shapes retrieval. Understanding shapes RAG.

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The architecture

Metric (cosine / L2 / dot).

ANN index (HNSW / IVF).

Filter by metadata.

Top-K retrieval.

Vector DB math foundationsDistance metriccosine / L2 / dotANN indexHNSW / IVF / etc.Filter + top-Kmetadata + retrieveCosine most common for embeddings; L2 for physical distance; dot for magnitude-aware
Vector DB math.
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How it works end to end

Metric matches embedding.

ANN trades accuracy for speed.

Filter integrated with index.