Linear Algebramath
The mathematics of vectors and matrices — vector spaces, dot products, norms, and linear transformations.
Embeddings live in vector spaces; similarity, projection, and dimensionality reduction are all linear algebra. It is the floor beneath most of SKC's semantic machinery.
Where it appears
- SKCE foundation link from embeddings
- vector-search
- cosine-similarity
Descend
Prerequisites
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Dependencies
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Foundations
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Historical evolution
Foundational since the 19th century; the engine of every modern embedding model.
Implementation details
Cosine similarity = (a.b)/(|a||b|); random-projection dimensionality reduction uses Uniform(-1,1) scaled by 2/sqrt(d).
Sources
- [2026-07-11-knowledge-compiler-compiling-human-knowledge-into-static-semantic-artifacts] 2026-07-11-knowledge-compiler-compiling-human-knowledge-into-static-semantic-artifacts
- [2026-07-11-knowledge-compiler-compiling-human-knowledge-into-static-semantic-artifacts] 2026-07-11-knowledge-compiler-compiling-human-knowledge-into-static-semantic-artifacts