New textbook teaches students about matrix methods and their real world applications

A new textbook, Linear Algebra for Data Science, Machine Learning, and Signal Processing, is being unveiled for use in classes that explore the many applications of matrix methods to real world data. Electrical and Computer Engineering (ECE) co-authors Jeffrey Fessler and Raj Nadakuditi have modeled the book after U-M’s ECE 551: Matrix Methods for Signal Processing, Data Analysis and Machine Learning, testing and refining the material with thousands of graduate students in the past decade.

“The goal of this class, and therefore the book, is to make sure that students can read the current literature on matrix-based methods for signal processing, machine learning, and data science,” explained Fessler, the William L. Root Collegiate Professor of Electrical Engineering and Computer Science (EECS). “It’s a big leap between what they’ve learned as an undergrad and that literature, so there has been a need for a book to help students with that bridge.”

Traditionally, ECE students have taken linear algebra courses in the math department or learned from math textbooks, where they solve equations but may learn less about their applications.

“In my own research and studies, it felt like the more I made contact with the application, the more I appreciated the theory and wanted to go deeper into it,” said Nadakuditi, associate professor of EECS. “I thought it was appropriate to introduce the theory alongside the application, rather than the traditional format––which is to first do all the theory and then the applications.”

Linear algebra explains how matrices add, multiply, and store information or patterns. Its applications, many of which are explored in Linear Algebra for Data Science, Machine Learning, and Signal Processing, include analyzing data recorded from multiple sensors simultaneously, recognizing handwritten digits, creating recommender systems such as those on Netflix or Spotify, conducting principal component analysis, and using neural networks.

The book also has a unique interactive component, with lots of online demos, engaging “explore” questions that allow students to check their understanding of concepts as they read, and coding problems in the Julia language.

“I hope all of these online real examples give students experience seeing how the equations relate to processing real data and help them understand the math better, as well,” said Fessler.

Thousands of students have learned the content of this book over the years, as Nadakuditi and Fessler developed and refined it with the help of graduate student instructors. They hope that math-loving engineering professors or engineering-loving math professors who want to teach these topics in their departments will adopt the textbook.

“Even the folks who know linear algebra are surprised at the different creative ways that you can apply it,” noted Nadakuditi.

In addition to the many graduate students who helped teach and refine the content, Fessler and Nadakuditi credit Zhongming Liu, associate professor of Biomedical Engineering and ECE, as well as UM alums Prof. Caroline Crockett, Prof. David Hong, Prof. Yong Long and researchers Jonas Kersulis, Brian Moore, and Simon Danisch for their various roles in the book’s development. Nadakuditi especially thanks Gil Strang and Alan Edelman for their encouragement and support as mentors and colleagues.

The authors donate a portion of their royalties from the book to organizations empowering historically marginalized groups in science, technology, engineering, and mathematics fields.

Linear Algebra for Data Science, Machine Learning, and Signal Processing is available for purchase at Cambridge University Press and Amazon.