Source Guide: Vectors and Linear Combinations
A curated source guide for learning vectors, span, and weighted combinations from first pass through research bridge.
Keywords
source guide, vectors, span, embeddings
1 How To Use This Guide
Use one source per layer:
First passfor intuition and basic fluencySecond passfor more exercises, operator language, or implementation flavorPaper bridgefor seeing vectors inside modern ML papers
Do not try to read the whole stack at once.
2 Stable Core
- MIT 18.06SC: Basis and Dimension -
First pass- strong official source for span, basis, and dimension as one storyline. Checked2026-04-24. - Introduction to Applied Linear Algebra – Vectors, Matrices, and Least Squares -
First pass- very good applied framing for vectors, combinations, and matrix-based thinking. Checked2026-04-24. - Hefferon, Linear Algebra -
Second pass- self-study depth with more proof and exercise practice. Checked2026-04-24.
3 Current Bridge
- Deep learning, transformers and graph neural networks: a linear algebra perspective -
Second pass- current bridge from vector-space basics to embeddings, attention, and graph models. Checked2026-04-24.
4 Paper Bridge
- Attention is All you Need -
Paper bridge- best first paper for seeing weighted vector mixtures become a central ML operation. Checked2026-04-24.
5 Recommended Reading Paths
5.1 Path 1: First serious understanding
- MIT 18.06SC Basis and Dimension
- Vectors and Linear Combinations
- Hefferon for extra exercises
5.2 Path 2: Vectors to modern representations
5.3 Path 3: Build intuition visually
6 Sources Checked Online
All links above were checked on 2026-04-24.
The verification pass included:
- official MIT OCW pages
- official Stanford or author-maintained textbook pages
- official NeurIPS proceedings page
- current journal page for the 2025 linear-algebra perspective survey