Advanced Linear Algebra
A Concise Text with Contemporary Applications

This engaging text helps advanced undergraduate students grasp core concepts in linear algebra and examines contemporary applications.

Yisong Yang (Author)

9781009589840, Cambridge University Press

Paperback / softback, published 12 June 2025

472 pages
22.9 x 15.1 x 2.6 cm, 0.69 kg

'It goes beyond mere computation, focusing on developing a conceptual understanding through proofs and real-world applications … this edition transforms the book into a dual-purpose resource: it remains a complete, theoretical course while simultaneously serving as a bridge to cutting-edge applications. It shows how deep mathematical fundamentals are essential for machine learning, data science, and quantum technology. Minor refinements and expanded exercises further enhance its classroom utility, solidifying its role in preparing students for academic and research endeavors at the forefront of science and engineering.' Mohammad Sal Moslehian, MathSciNet

The second edition of this engaging textbook for advanced undergraduate students and beginning graduates covers all the core subjects in linear algebra. It has a unique emphasis on integrating ideas from analysis, in addition to pure algebra, and features a balance of abstraction, practicality, and contemporary applications. Four chapters examine some of the most important of these applications, including quantum mechanics, machine learning, data science, and quantum information. The material is supplemented by a rich collection of exercises designed for students from diverse backgrounds, including a wealth of newly added ones in this edition. Selected solutions are provided at the back of the book for use in self-study, and full solutions are available online to instructors.

Notation and convention
1. Vector spaces
2. Linear mappings
3. Determinants
4. Scalar products
5. Real quadratic forms and self-adjoint mappings
6. Complex quadratic forms and self-adjoint mappings
7. Jordan decomposition
8. Selected topics
9. Excursion: Quantum mechanics in a nutshell
10. Excursion: Problems in machine learning
11. Excursion: Problems in data analysis
12. Excursion: Multilinear algebra
13. Excursion: Essentials of quantum information and quantum entanglement
Solutions to selected problems
Bibliographic notes
Bibliography
Index.

Subject Areas: Algebra [PBF]