Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares

Stephen Boyd and Lieven Vandenberghe

Digital versions PDF
Latex source No
Exercises Yes
Answers and hints No
License Copyright by Cambridge Univ. Press
  • Text for a first course in linear algebra
  • Emphasis on topics and applications for computer science and engineering
  • In use at Stanford, UCLA, and elsewhere
  • 473 pages, 19 chapters
  • Hardcover version for about $50
  • Additional exercises, lecture slides, and Julia companion
  • For more information and to download

This textbook is loaded with applications relevant today for areas such as machine learning and data analysis, and it provides the mathematical and conceptual foundations necessary to understand them. The entire book can be covered in a single semester. Fewer mathematical topics are covered than usual for a linear algebra course, but the coverage is deeper than usual for a first course. From the preface:

We use only one theoretical concept from linear algebra, linear independence, and only one computational tool, the QR factorization; our approach to most applications relies on only one method, least squares (or some extension). In this sense we aim for intellectual economy…

There is, however, no material on determinants, eigenvalues, and eigenvectors—standard topics in linear algebra courses in math departments, and so an instructor would need to provide supplementary material for those topics. On the other hand, this book could be a valuable secondary source for a standard math course.

Table of Contents


  1. Vectors
  2. Linear functions
  3. Norm and distance
  4. Clustering
  5. Linear independence

  1. Matrices
  2. Matrix examples
  3. Linear equations
  4. Linear dynamical systems
  5. Matrix multiplication
  6. Matrix inverses
Least squares

  1. Least squares
  2. Least squares data fitting
  3. Least squares classification
  4. Multi-objective least squares
  5. Constrained least squares
  6. Constrained least squares applications
  7. Nonlinear least squares
  8. Constrained nonlinear least squares