Advanced linear algebra

✍ Scribed by Woerdeman, Hugo Jan

• Publisher: CRC Press
• Year: 2016
• Tongue: English
• Leaves: 348
• Series: Textbooks in mathematics (Boca Raton Fla.)
• Category: Library

✦ Synopsis

Advanced Linear Algebra features a student-friendly approach to the theory of linear algebra. The authors 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. --back cover.  Read more...

✦ Table of Contents

1. Fields and matrix algegra --
   2. Vector spaces --
   3. Linear transformations --
   4. the Jordan canonical form --
   5. Inner product and normed vector spaces --
   6. Constructing new vector spaces from given ones --
   7. How to use liear algebra --
   How to start your own research project --
   Answers to exercises.

✦ Subjects

Algebras, Linear