Andre Lukas

The Oxford Linear Algebra for Scientists (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Oxford University Press
• Seitenzahl: 432
• Erscheinungstermin: 12. Mai 2022
• Englisch
• ISBN-13: 9780192583475
• Artikelnr.: 64044068

Autorenporträt

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.

Inhaltsangabe

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