Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (17 chapters)
-
Preliminaries
-
Basic Linear Algebra
-
Topics
Keywords
About this book
This book is a thorough introduction to linear algebra, for the graduate or advanced undergraduate student. Prerequisites are limited to a knowledge of the basic properties of matrices and determinants. However, since we cover the basics of vector spaces and linear transformations rather rapidly, a prior course in linear algebra (even at the sophomore level), along with a certain measure of "mathematical maturity," is highly desirable. Chapter 0 contains a summary of certain topics in modern algebra that are required for the sequel. This chapter should be skimmed quickly and then used primarily as a reference. Chapters 1-3 contain a discussion of the basic properties of vector spaces and linear transformations. Chapter 4 is devoted to a discussion of modules, emphasizing a comparison between the properties of modules and those of vector spaces. Chapter 5 provides more on modules. The main goals of this chapter are to prove that any two bases of a free module have the same cardinality and to introduce noetherian modules. However, the instructor may simply skim over this chapter, omitting all proofs. Chapter 6 is devoted to the theory of modules over a principal ideal domain, establishing the cyclic decomposition theorem for finitely generated modules. This theorem is the key to the structure theorems for finite dimensional linear operators, discussed in Chapters 7 and 8. Chapter 9 is devoted to real and complex inner product spaces.
Authors and Affiliations
Bibliographic Information
Book Title: Advanced Linear Algebra
Authors: Steven Roman
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-1-4757-2178-2
Publisher: Springer New York, NY
-
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag New York 1992
eBook ISBN: 978-1-4757-2178-2Published: 09 March 2013
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 1
Number of Pages: XII, 370