Vectors, pure and applied
Subtitle: a general introduction to linear algebra
By: T.W. Körner, Trinity Hall, Cambridge
Publisher: Cambridge University Press
Published: 2013
Place of publication: Cambridge
Language: eng
Number of pages: 444
ISBN-13: 9781107033566; 9781107675223
Subjects: Linear Algebras; Vector algebra; MATHEMATICS / Algebra / General
Description: "Many books in linear algebra focus purely on getting students through exams, but this text explains both the how and the why of linear algebra and enables students to begin thinking like mathematicians. The author demonstrates how different topics (geometry, abstract algebra, numerical analysis, physics) make use of vectors in different ways and how these ways are connected, preparing students for further work in these areas. The book is packed with hundreds of exercises ranging from the routine to the challenging. Sketch solutions of the easier exercises are available online"--
Notes: Includes bibliographical references (pages 438-439) and index.
Table of contents: title: Machine generated contents note: Introduction; Part I. Familiar Vector Spaces: 1. Gaussian elimination; 2. A little geometry; 3. The algebra of square matrices; 4. The secret life of determinants; 5. Abstract vector spaces; 6. Linear maps from Fn to itself; 7. Distance preserving linear maps; 8. Diagonalisation for orthonormal bases; 9. Cartesian tensors; 10. More on tensors; Part II. General Vector Spaces: 11. Spaces of linear maps; 12. Polynomials in L(U,U); 13. Vector spaces without distances; 14. Vector spaces with distances; 15. More distances; 16. Quadratic forms and their relatives; Bibliography; Index.