Introduction to Linear Algebra with Earth Science Applications

Hello, I am Benjamin Loi from CUHK-EESC and NTU-AS. This is the repository for the tex/python files for my book Introduction to Linear Algebra with Earth Science Applications.

The book pdf is located at here (First Edition).

Meanwhile, the Jupyter notebooks are placed in this folder.

This project has been completed in May 2025.

Contributing to the Project

Feel free to open an issue regarding any problem or suggestion about the book! Any idea will be greatly appreciated. When the book is completed, I will upload it to ArXiv formally for open access. This repository will stay open anyway.

Table of Content

1. Introduction to Matrices and Linear Systems
2. Inverses and Determinants
3. Solutions for Linear Systems
4. Introduction to Vectors
5. Vector Geometry
6. Vector Spaces and Coordinate Bases
7. More on Coordinate Bases, Linear Transformations
8. Complex Vectors/Matrices and Block Matrices
9. Eigenvalues and Eigenvectors
10. Orthogonal and Normal Matrices
11. Quadratic Forms
12. Inner Product Spaces
13. Least-Square Approximation
14. Discrete Fourier Transform (DFT)
15. Markov Chains
16. Matrix Factorization Methods
17. Dynamical Systems
18. Index Notation and Introduction to Tensors

Appendix

• Cyclic Subspaces and Jordan Normal Forms

Printed Version

Click here (Amazon) to purchase a hardcover version to support my effort!

Cite this Work

Loi, C. L. Introduction to Linear Algebra with Earth Science Applications. 2025. ISBN: 9786260139902.