Vectors, Matrices, and Embeddings

中文导读

这篇文章的目标不是重讲线性代数课本，而是回答一个更实用的问题：为什么向量和矩阵会一直出现在机器学习、NLP、LLM 和 retrieval 里？

Working outline

1. What a vector means in ML
2. Why embeddings are vectors
3. Dot product and cosine similarity
4. Matrix multiplication as transformation
5. Neural layers as learned transformations
6. Retrieval as geometry

Reference materials to digest

• Deep Learning Book: Linear Algebra
• Stanford CS229: Linear Algebra Review
• Hugging Face Course

My angle

I want this post to explain linear algebra through examples I actually use:

• sentence embeddings;
• nearest-neighbor search;
• attention scores;
• retrieval systems;
• dimensionality reduction for error analysis.