Source Guide: Matrices and Linear Maps
A curated source guide for learning matrices as linear maps from first pass through research bridge.
Keywords
source guide, matrices, linear maps, operators
1 How To Use This Guide
Use one source per layer:
First passfor the operator viewpointSecond passfor extra exercises and coordinate disciplinePaper bridgefor seeing matrices inside modern systems
2 Stable Core
- MIT 18.06SC: Linear Transformations and their Matrices -
First pass- best official source for the core theorem that columns are basis images. Checked2026-04-24. - Introduction to Applied Linear Algebra – Vectors, Matrices, and Least Squares -
First pass- good applied treatment of transformations and matrix computation. Checked2026-04-24. - Hefferon, Linear Algebra -
Second pass- stronger proof and exercise depth for linear maps and coordinate representations. Checked2026-04-24.
3 Current Bridge
- Deep learning, transformers and graph neural networks: a linear algebra perspective -
Second pass- current survey showing how operator language remains useful in AI systems. Checked2026-04-24.
4 Paper Bridge
- Attention is All you Need -
Paper bridge- canonical architecture paper where learned projections are explicit matrix maps. Checked2026-04-24.
5 Recommended Reading Paths
5.1 Path 1: First serious understanding
- MIT 18.06SC Linear Transformations and their Matrices
- Matrices and Linear Maps
- Hefferon for extra exercises
5.2 Path 2: Operator intuition with visuals
5.3 Path 3: Bridge to modern ML systems
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