Advanced Linear Algebra

A Concise Text with Contemporary Applications

Yisong Yang (New York University)

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English

Cambridge University Press
30 June 2025

Mathematics & Sciences; Algebra

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 more than 550 exercises suitable for students from a wide variety of backgrounds, including over 200 exercises new to 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.

By: Yisong Yang (New York University)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Edition: 2nd Revised edition
ISBN: 9781009589840
ISBN 10: 1009589849
Pages: 465
Publication Date: 30 June 2025
Format: Paperback
Publisher's Status: Forthcoming

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.

Yisong Yang is Professor at the Courant Institute of Mathematical Sciences, New York University. He is a Fellow of the American Mathematical Society and the author of 'Solitons in Field Theory and Nonlinear Analysis' (2001) and 'Mathematical Physics with Differential Equations' (2023).