Advanced Linear Algebra
Advanced Linear Algebra
$49.99
USDThe 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.
- Covers all the core topics of linear algebra, approaching many from the viewpoint of analysis
- Contains a rich collection of exercises, with a full solution manual available to instructors at www.cambridge.org/Yang2e
- Features chapters tackling important contemporary applications, including quantum mechanics, machine learning, data science, and quantum information
- Well-motivated presentation avoids unnecessary abstraction, giving readers a clear grasp of the concepts, supplemented with concrete examples where necessary
- Demonstrates connections between linear algebra and other important areas
Reviews & endorsements
'Mastering the intricacies of linear algebra has never been easier. This textbook offers a clear, engaging approach that demystifies complex concepts while providing some contemporary applications in quantum mechanics, machine learning, and data science. A valuable resource for both students and professionals eager to deepen their understanding of this foundational discipline!' Jichun Li, University of Nevada, Las Vegas
'Yang's book is a wonderful introduction to linear algebra. It is simultaneously precise and casual and covers both introductory and advanced material. This second edition includes fantastic excursions into areas of mathematics and physics where linear algebra plays a central role, such as quantum information theory and machine learning, providing the reader a unique opportunity to see the material they just learned put to good use. I highly recommend this text.' Isaac M. Goldbring, University of California, Irvine
Product details
June 2025Paperback
9781009589840
472 pages
229 × 152 mm
0.68kg
Not yet published - available from May 2025
Table of Contents
- 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.
