The Oxford Linear Algebra for Scientists

1. Auflage 2022
ISBN: 978-0-19-884491-4
Verlag: Oxford University Press

Buch, Englisch, 432 Seiten, Format (B × H): 180 mm x 253 mm, Gewicht: 978 g

This textbook provides a modern introduction to linear algebra, a mathematical discipline every first year undergraduate student in physics and engineering must learn. A rigorous introduction into the mathematics is combined with many examples, solved problems, and exercises as well as scientific applications of linear algebra. These include applications to contemporary topics such as internet search, artificial intelligence, neural networks, and quantum computing, as well as a number of more advanced topics, such as Jordan normal form, singular value decomposition, and tensors, which will make it a useful reference for a more experienced practitioner.

Structured into 27 chapters, it is designed as a basis for a lecture course and combines a rigorous mathematical development of the subject with a range of concisely presented scientific applications. The main text contains many examples and solved problems to help the reader develop a working knowledge of the subject and every chapter comes with exercises.

Autoren/Hrsg.

Lukas, Andre

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Physik Mechanik
• Mathematik | Informatik Mathematik Algebra

Inhaltsverzeichnis

- 1: Linearity - an informal introduction

- 2: Sets and functions

- 3: Groups

- 4: Fields

- 5: Coordinate vectors

- 6: Vector spaces

- 7: Elementary vector space properties

- 8: Vector subspaces

- 9: The dot product

- 10: Vector and triple product

- 11: Lines and planes

- 12: Introduction to linear maps

- 13: Matrices

- 14: The structure of linear maps

- 15: Linear maps in terms of matrices

- 16: Computing with matrices

- 17: Linear systems

- 18: Determinants

- 19: Basics of eigenvalues

- 20: Diagonalising linear maps

- 21: The Jordan normal form

- 22: Scalar products

- 23: Adjoint and unitary maps

- 24: Diagonalisation - again

- 25: Bi-linear and sesqui-linear forms

- 26: The dual vector space

- 27: Tensors

Über Autor(innen)

Andre Lukas graduated in physics at the University of Wuppertal in 1991 and received his doctoral degree at the Technical University of Munich in 1995, before moving on to postdoctoral positions at the University of Pennsylvania and the University of Oxford. After a period as a member of faculty at the University of Sussex he returned to the University of Oxford in 2004 where he is currently a Professor of Theoretical Physics. His main area of research is string theory and its relation to differential and algebraic geometry.