Advanced Linear Algebra:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1992
|
| Series: | Graduate Texts in Mathematics
135 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | 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 |
| Physical Description: | 1 Online-Ressource (XII, 370 p) |
| ISBN: | 9781475721782 9781475721805 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4757-2178-2 |
Staff View
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| spelling | Roman, Steven Verfasser aut Advanced Linear Algebra by Steven Roman New York, NY Springer New York 1992 1 Online-Ressource (XII, 370 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 135 0072-5285 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 Mathematics Matrix theory Linear and Multilinear Algebras, Matrix Theory Mathematik Lineare Algebra (DE-588)4035811-2 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Lineare Algebra (DE-588)4035811-2 s 2\p DE-604 https://doi.org/10.1007/978-1-4757-2178-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Roman, Steven Advanced Linear Algebra Mathematics Matrix theory Linear and Multilinear Algebras, Matrix Theory Mathematik Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4035811-2 (DE-588)4123623-3 |
| title | Advanced Linear Algebra |
| title_auth | Advanced Linear Algebra |
| title_exact_search | Advanced Linear Algebra |
| title_full | Advanced Linear Algebra by Steven Roman |
| title_fullStr | Advanced Linear Algebra by Steven Roman |
| title_full_unstemmed | Advanced Linear Algebra by Steven Roman |
| title_short | Advanced Linear Algebra |
| title_sort | advanced linear algebra |
| topic | Mathematics Matrix theory Linear and Multilinear Algebras, Matrix Theory Mathematik Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Mathematics Matrix theory Linear and Multilinear Algebras, Matrix Theory Mathematik Lineare Algebra Lehrbuch |
| url | https://doi.org/10.1007/978-1-4757-2178-2 |
| work_keys_str_mv | AT romansteven advancedlinearalgebra |