This expanded and revamped second edition follows an excellent first edition, and is the culmination of classroom experiences since the first edition’s publication more than two decades ago. While the two editions share the same title, this new edition is longer by 250-plus pages. It is divided into eight long chapters and an appendix.

Starting with definitions for linear algebra and applied linear algebra, chapter 1 introduces various operations on vectors and matrices. The fundamentals of Gaussian elimination are thoroughly covered in chapter 2. Chapter 3, “Eigensystem Basis,” covers diagonalizability, singular value decomposition (SVD), and quadratic forms. The basic theory of vector spaces is discussed in chapter 4. Chapter 5, on inner product spaces and Fourier expansion, develops QR factorization and introduces discrete Fourier transforms. Algorithms for computing eigenvalues, including the power method and QR iterations, form the core of chapter 6. Chapter 7 contains a detailed development of the Perron–Frobenius theorem of nonnegative matrices and its application to Markov chain theory. Chapter 8, on matrix analysis via resolvent calculus, is new to the second edition and deals with the sensitivity analysis of eigenvalues with respect to the elements of the matrices. The first edition’s chapter 6, “An Overview of Determinants,” is now relegated to the appendix in this second edition.

There are two hallmarks of this edition: the number of worked examples and exercise problems; and the addition of historical comments, along with pictures of the original authors, adds to its charm and readability. References are embedded as footnotes when appropriate. An extensive 21-page index allows for easy navigation through this bulky volume.

Depending on the interest, one can either build a one-semester introductory course on linear algebra for advanced undergraduates or cover the entire book in a two-semester sequence with detailed programming projects. This expanded edition includes extensive coverage of applications relevant to the new and evolving data science and analytics curriculum. This book is a great addition to the literature; serious students of mathematics, engineering, computer science, data analytics, and artificial intelligence/machine learning (AI/ML) should have it in their personal library.