The Linear Algebra a Beginning Graduate Student Ought to Know / Edition 3

The Linear Algebra a Beginning Graduate Student Ought to Know / Edition 3

by Jonathan S. Golan
     
 

ISBN-10: 940072635X

ISBN-13: 9789400726352

Pub. Date: 03/16/2012

Publisher: Springer Netherlands

Linear algebra is a living, active branch of mathematics which is central to almost all other areas of mathematics, both pure and applied, as well as computer science, the physical and social sciences, and engineering. It entails an extensive corpus of theoretical results as well as a large body of computational techniques.

The book is intended to be used in one

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Overview

Linear algebra is a living, active branch of mathematics which is central to almost all other areas of mathematics, both pure and applied, as well as computer science, the physical and social sciences, and engineering. It entails an extensive corpus of theoretical results as well as a large body of computational techniques.

The book is intended to be used in one of several possible ways:

(1) as a self-study guide;

(2) as a textbook for a course in advanced linear algebra, either at the upper-class undergraduate level or at the first-year graduate level; or

(3) as a reference book.

It is also designed to prepare a student for the linear algebra portion of prelim exams or PhD qualifying exams.

The volume is self-contained to the extent that it does not assume any previous formal knowledge of linear algebra, though the reader is assumed to have been exposed, at least informally, to some basic ideas and techniques, such as the solution of a small system of linear equations over the real numbers. More importantly, it does assume a seriousness of purpose and a modicum of mathematical sophistication. The book also contains over 1000 exercises, many of which are very challenging.

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Product Details

ISBN-13:
9789400726352
Publisher:
Springer Netherlands
Publication date:
03/16/2012
Edition description:
3rd ed. 2012
Pages:
497
Sales rank:
655,044
Product dimensions:
6.10(w) x 9.20(h) x 1.20(d)

Table of Contents

1. Notation and terminology.- 2. Fields.- 3. Vector spaces over a field.- 4. Algebras over a field.- 5. Linear Dependence and Dimension.- 6. Linear Transformations.- 7. The endomorphism algebra of a vector space.- 8. Representation of linear transformations by matrices.- 9. The algebra of square matrices.- 10. Systems of linear equations.- 11.Determinants.- 12. Eigenvalues and eigenvectors.- 13. Krylov subspaces.- 14. The dual space.- 15. Inner product spaces.- 16. Orthogonality.- 17. Selfadjoint endomorphisms.- 18. Unitary and normal endomorphisms.- 19. Moore-Penrose pseudoinverses.- 20. Bilinear transformations and forms.

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