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The Oxford Linear Algebra for Scientists

Andre Lukas

June 2022

ISBN: 9780198844921

432 pages
Paperback
246x171mm

In Stock

Price: £24.99

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.

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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