Matrix Methods in Data Analysis

This textbook offers a fresh and balanced approach to the study of Linear Algebra in the context of modern Data Science. Whereas many existing texts either emphasize theory with little connection to practice or jump straight to applications with minimal mathematical explanation, this book provides equal weight to both foundations and applications.

Designed for undergraduates who have completed a proof-based Linear Algebra course, it introduces concepts and tools from Matrix Analysis that are essential for Data Science and Machine Learning. Topics include:

• Vector norms and distances, orthogonality, and projections
• Matrix factorizations such as LU, CR, QR, and SVD
• Special matrix types: symmetric, positive definite, nonnegative, stochastic, and covariance matrices
• Key numerical algorithms, including the QR algorithm and the Power Method

Each chapter is enriched with real-world applications—from Google PageRank and Principal Component Analysis to clustering, dimensionality reduction, and linear regression—highlighting the role of matrix methods in Data Science.

To further support hands-on learning, the book is accompanied by a GitHub repository with Python labs, allowing students to implement the techniques covered and bridge the gap between theory and computation.

With its clear explanations, practical insights, and balance of theory and application, Matrix Methods in Data Analysis is an invaluable resource for courses in applied Linear Algebra, Data Science, and introductory Machine Learning.

Maria Isabel Bueno is a Teaching Professor at the University of California, Santa Barbara, where she has served since 2006. She holds a Ph.D. from Universidad Carlos III de Madrid. Her research focuses on linear algebra and numerical linear algebra.

Javier Perez Alvaro is an Associate Professor at the University of Montana in Missoula, where he has served since 2017. He earned his Ph.D. from Universidad Carlos III de Madrid. His research focuses on numerical linear algebra and numerical analysis.