The Oxford Linear Algebra for Scientists

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Andre Lukas (Professor of Theoretical Physics, Professor of Theoretical Physics, University of Oxford)

The Oxford Linear Algebra for Scientists

Andre Lukas (Professor of Theoretical Physics, Professor of Theoretical Physics, University of Oxford)

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English

Oxford University Press
01 September 2022

Algebra; Classical mechanics; Mathematical physics

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.

By: Andre Lukas (Professor of Theoretical Physics Professor of Theoretical Physics University of Oxford)
Imprint: Oxford University Press
Country of Publication: United Kingdom
Edition: 1
Dimensions: Height: 250mm, Width: 175mm, Spine: 28mm
Weight: 970g
ISBN: 9780198844914
ISBN 10: 0198844913
Pages: 432
Publication Date: 01 September 2022
Audience: College/higher education , Primary
Format: Hardback
Publisher's Status: Active

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

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.

Reviews for The Oxford Linear Algebra for Scientists

The authors are uniquely well qualified to produce a textbook suitable for first-year university students. * David Matravers, University of Portsmouth * Linear Algebra is a core undergraduate course not only in Mathematics but also in Physics, Chemistry, Biology and Computer Science. This textbook brilliantly succeeds in catering to such a wide audience by covering a broad range of formal developments along with concrete applications and is unique in its presentation of the topic. * Richard Joseph Szabo, Heriot-Watt University * Lukas has written an impressive mathematical textbook that covers standard introductory linear algebra topics along with advanced concepts that will appeal to many readers. * Choice *