A (Terse) Introduction to Linear Algebra
About this Title
Yitzhak Katznelson, Stanford University, Stanford, CA and Yonatan R. Katznelson, University of California, Santa Cruz, Santa Cruz, CA
Publication: The Student Mathematical Library
Publication Year 2008: Volume 44
ISBNs: 978-0-8218-4419-9 (print); 978-1-4704-1218-0 (online)
MathSciNet review: MR2374064
MSC: Primary 15-01
Linear algebra is the study of vector spaces and the linear maps between them. It underlies much of modern mathematics and is widely used in applications.
A (Terse) Introduction to Linear Algebra is a concise presentation of the core material of the subject—those elements of linear algebra that every mathematician, and everyone who uses mathematics, should know. It goes from the notion of a finite-dimensional vector space to the canonical forms of linear operators and their matrices, and covers along the way such key topics as: systems of linear equations, linear operators and matrices, determinants, duality, and the spectral theory of operators on inner-product spaces.
The last chapter offers a selection of additional topics indicating directions in which the core material can be applied.
The Appendix provides all the relevant background material.
Written for students with some mathematical maturity and an interest in abstraction and formal reasoning, the book is self-contained and is appropriate for an advanced undergraduate course in linear algebra.
Undergraduate and graduate students interested in linear algebra.
Table of Contents
- Chapter 1. Vector spaces
- Chapter 2. Linear operators and matrices
- Chapter 3. Duality of vector spaces
- Chapter 4. Determinants
- Chapter 5. Invariant subspaces
- Chapter 6. Inner-product spaces
- Chapter 7. Structure theorems
- Chapter 8. Additional topics