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The Linear Algebra a Beginning Graduate Student Ought to Know

  • Textbook
  • © 2012

Overview

Authors:
  1. Jonathan S. Golan

    1. Dept. Math & Computer Science, University of Haifa, Haifa, Israel

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  • Contains a wealth of biographical notes and thumbnail photos
  • Facilitates the transition from concrete exemplification to theoretical abstraction and thus enables a deeper level of understanding for use in a real world context
  • 131 exercises have been added to the already extensive collection supplied in the 2nd edition
  • Can be used as a self-study guide, textbook or reference work
  • Includes supplementary material: sn.pub/extras

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Table of contents (20 chapters)

  1. Front Matter

    Pages I-XI
    Download chapter PDF

  2. Notation and Terminology

    • Jonathan S. Golan
    Pages 1-3

  3. Fields

    • Jonathan S. Golan
    Pages 5-19

  4. Vector Spaces Over a Field

    • Jonathan S. Golan
    Pages 21-38

  5. Algebras Over a Field

    • Jonathan S. Golan
    Pages 39-56

  6. Linear Independence and Dimension

    • Jonathan S. Golan
    Pages 57-88

  7. Linear Transformations

    • Jonathan S. Golan
    Pages 89-111

  8. The Endomorphism Algebra of a Vector Space

    • Jonathan S. Golan
    Pages 113-131

  9. Representation of Linear Transformations by Matrices

    • Jonathan S. Golan
    Pages 133-146

  10. The Algebra of Square Matrices

    • Jonathan S. Golan
    Pages 147-188

  11. Systems of Linear Equations

    • Jonathan S. Golan
    Pages 189-220

  12. Determinants

    • Jonathan S. Golan
    Pages 221-253

  13. Eigenvalues and Eigenvectors

    • Jonathan S. Golan
    Pages 255-296

  14. Krylov Subspaces

    • Jonathan S. Golan
    Pages 297-316

  15. The Dual Space

    • Jonathan S. Golan
    Pages 317-332

  16. Inner Product Spaces

    • Jonathan S. Golan
    Pages 333-367

  17. Orthogonality

    • Jonathan S. Golan
    Pages 369-394

  18. Selfadjoint Endomorphisms

    • Jonathan S. Golan
    Pages 395-418

  19. Unitary and Normal Endomorphisms

    • Jonathan S. Golan
    Pages 419-440

  20. Moore–Penrose Pseudoinverses

    • Jonathan S. Golan
    Pages 441-452
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Keywords

About this book

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.

Reviews

From the reviews of the third edition:

“This edition is enhanced by the inclusion of further results and many new examples. There are also over 130 additional exercises and many of the earlier ones have been revised. Furthermore, many more biographical notes and thumbnail portraits of mathematicians connected in some way with linear algebra have been added. This book continues to be very successful and useful, not only as a textbook for advanced linear algebra courses, but also for self-study and reference purposes.” (Rabe von Randow, Zentralblatt MATH, Vol. 1237, 2012)

Authors and Affiliations

  • Dept. Math & Computer Science, University of Haifa, Haifa, Israel

    Jonathan S. Golan

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