Advanced Linear Algebra (eBook)

Steven Roman (Autor)

eBook Download: PDF

2013
Springer New York (Verlag)
978-1-4757-2178-2 (ISBN)

Infos

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 "e;mathematical maturity,"e; 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.

Produkt-Details

• Erscheint lt. Verlag: 9.3.2013
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• ISBN-10: 1-4757-2178-1 / 1475721781
• ISBN-13: 978-1-4757-2178-2 / 9781475721782