Advanced Linear Algebra

✍ Scribed by Hugo Woerdeman

• Publisher: CRC Press
• Year: 2015
• Tongue: English
• Leaves: 348
• Series: Textbooks in Mathematics
• Category: Library

✦ Synopsis

Advanced Linear Algebra features a student-friendly approach to the theory of linear algebra. The author’s emphasis on vector spaces over general fields, with corresponding current applications, sets the book apart. He focuses on finite fields and complex numbers, and discusses matrix algebra over these fields. The text then proceeds to cover vector spaces in depth. Also discussed are standard topics in linear algebra including linear transformations, Jordan canonical form, inner product spaces, spectral theory, and, as supplementary topics, dual spaces, quotient spaces, and tensor products.

Written in clear and concise language, the text sticks to the development of linear algebra without excessively addressing applications. A unique chapter on "How to Use Linear Algebra" is offered after the theory is presented. In addition, students are given pointers on how to start a research project. The proofs are clear and complete and the exercises are well designed. In addition, full solutions are included for almost all exercises.

✦ Table of Contents

Front Cover
Contents
Preface to the Instructor
Preface to the Student
Acknowledgments
Notation
List of Figures
Chapter 1: Fields and Matrix Algebra
Chapter 2: Vector Spaces
Chapter 3: Linear Transformations
Chapter 4: The Jordan Canonical Form
Chapter 5: Inner Product and Normed Vector Spaces
Chapter 6: Constructing New Vector Spaces from Given Ones
Chapter 7: How to Use Linear Algebra
How to Start Your Own ResearchProject
Answers to Exercises
Bibliography
Back Cover