Advanced Linear Algebra

2. Auflage 2025
ISBN: 978-1-009-58984-0
Verlag: Cambridge University Press

Buch, Englisch, 472 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 626 g

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.

Autoren/Hrsg.

Yang, Yisong

Inhaltsverzeichnis

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.

Über Autor(innen)

Yang, Yisong
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).