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 files for my book Introduction to Linear Algebra with Earth Science Applications.

The book pdf is located at here.

This project is still alive and being constantly updated as of Nov 2024.

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 anyways.

Table of Content (Draft)

(inside brackets are the expected finish and upload dates)

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, Diagonalization
10. Orthogonal and Normal Matrices
11. Quadratic Form
12. Inner Product Space
13. Least-Square Approximation
14. Discrete Fourier Transform
15. Markov Chains
16. Matrix Factorization Methods
17. Dynamical Systems (2025-01-15)
18. Index Notation and Introduction to Tensor (2025-02-15)

Appendix

• Jordan Normal Form