Linear Algebra a Beginning Graduate Student Ought to Know 3th The Mostafa

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Product details:

• ISBN 10: 9400726368
• ISBN 13: 9789400726369 
• Author: Jonathan S. Golan
  

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 to computer science, to the physical, biological, and social sciences, and to engineering. It encompasses an extensive corpus of theoretical results as well as a large and rapidly-growing body of computational techniques. Unfortunately, in the past decade, the content of linear algebra courses required to complete an undergraduate degree in mathematics has been depleted to the extent that they fail to provide a sufficient theoretical or computational background. Students are not only less able to formulate or even follow mathematical proofs, they are also less able to understand the mathematics of the numerical algorithms they need for applications. Certainly, the material presented in the average undergraduate course is insufficient for graduate study. This book is intended to fill the gap which has developed by providing enough theoretical and computational material to allow the advanced undergraduate or beginning graduate student to overcome this deficiency and be able to work independently or in advanced courses. The book is intended to be used either as a self-study guide, a textbook for a course in advanced linear algebra, or 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 of the basic ideas and techniques, such as manipulation of small matrices and the solution of small systems of linear equations over the real numbers. More importantly, it assumes a seriousness of purpose, considerable motivation, and a modicum of mathematical sophistication on the part of the reader. In the latest edition, new major theorems have been added, as wellas many new examples. There are over 130 additional exercises and many of the previous exercises have been revised or rewritten. In addition, a large number of additional biographical notes and thumbnail portraits of mathematicians have been included.

Table contents:

Part 1. Notation and Terminology
Part 2. Fields
Part 3. Vector Spaces Over a Field
Part 4. Algebras Over a Field
Part 5. Linear Independence and Dimension
Part 6. Linear Transformations
Part 7. The Endomorphism Algebra of a Vector Space
Part 8. Representation of Linear Transformations by Matrices
Part 9. The Algebra of Square Matrices
Part 10. Systems of Linear Equations
Part 11. Determinants
Part 12. Eigenvalues and Eigenvectors
Part 13. Krylov Subspaces
Part 14. The Dual Space
Part 15. Inner Product Spaces
Part 16. Orthogonality
Part 17. Selfadjoint Endomorphisms
Part 18. Unitary and Normal Endomorphisms
Part 19. Moore–Penrose Pseudoinverses
Part 20. Bilinear Transformations and Forms

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