Intro to LinAlg Earth

<h1>Introduction to Linear Algebra with Earth Science Applications</h1>

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

<b>The book pdf is located at here (First Edition).</b>

Meanwhile, the Jupyter notebooks are placed in this folder.

This project has been completed in May 2025.

<h2>Contributing to the Project</h2>

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.
Update: There will be a minor patch to integrate all the comments in the near future.

<h2>Table of Contents</h2>

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

<h2>Printed Version</h2>

Below are several possible channels to purchase a hardcover version to support my effort if you like the book!

• Barnes and Noble
• Amazon (In some regions, there may be difficulty with shipping the book. If so, use the Barnes and Noble channel above.)
• 天瓏 (Taiwan only)

<h2>Cite this Work</h2>

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

Shield:

This work is licensed under a
Creative Commons Attribution-NonCommercial 4.0 International License.