Cover
Title Page
Copyright Page
Dedication
Table of Contents
Preface to the Instructor
Preface to the Student
Acknowledgments
Notation
List of Figures
1 Fields and Matrix Algebra
1.1 The field ℤ3
1.2 The field axioms
1.3 Field examples
1.3.1 Complex numbers
1.3.2 The finite field ℤp, with p prime
1.4 Matrix algebra over different fields
1.4.1 Reminders about Cramer’s rule and the adjugate matrix.
1.5 Exercises
2 Vector Spaces
2.1 Definition of a vector space
2.2 Vector spaces of functions
2.2.1 The special case when X is finite
2.3 Subspaces and more examples of vector spaces

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.

English