Introduction to Linear Algebra with Earth Science Applications

This is a Linear Algebra textbook specifically designed for students who are majoring in any Earth Science-related subjects like Geophysics and Atmospheric Sciences, and are also interested in Mathematics. With these target readers in mind, we set out to provide an adequate treatment of Linear Algebra concepts that enables them to tackle relevant Earth Science problems. It aims at striking a balance between mathematical theories and physical (mainly Earth Science) applications.

For the first part, it contains a comprehensive review of

• Matrix and Vector Operations
• Vector (Inner Product) Spaces and Linear Transformations
• Eigenvalues/Eigenvectors and Diagonalization, and more

Meanwhile, the topics of the second part include:

• Principal Component Analysis (PCA)
• Least-square Linear Regression
• Discrete Fourier Transform (DFT)
• Markov Chains
• Matrix Factorization Methods such as Cholesky/L(D)U/SVD
• Dynamical Systems
• Continuum Mechanics
• Data Assimilation

In each chapter, we focus on a selected Linear Algebra topic, motivated by Earth Science examples (if available) and supplemented with Python programming tutorials. At the end of each chapter, a number of exercises (answered, a total of 136) are given for elucidating the concepts and working on Earth Science projects. This book also provides several colored figures for illustration.