The Oxford Linear Algebra for Scientists

Description

Aimed at first-year undergraduate student in physics and engineering, this textbook combines a rigorous theoretical introduction to linear algebra with many examples, solved problems, and exercises, as well as scientific applications of the subject, including internet search, artificial intelligence, and quantum computing.

• Based on a first year undergraduate lecture course at Oxford University
• Includes end-of-chapter exercises and solved problems for students to test their understanding
• Discusses the modern applications of linear algebra in areas such as AI and quantum computing

About the Author(s)

Andre Lukas, Professor of Theoretical Physics, University of Oxford

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.

Table of Contents

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

Reviews

"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