抽象代数讲义（第2卷）（英文）

图书标准信息

• 作者 [德]雅格布斯（Jacobson N.） 著
• 出版社 世界图书出版公司
• 出版时间 2013-10
• 版次 1
• ISBN 9787510061523
• 定价 59.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 280页
• 正文语种 英语

【内容简介】

　　Thepresentvolumeisthesecondintheauthor'sseriesofthreedealingwithabstractalgebra.ForanunderstandingofthisvolumeacertainfamiliaritywiththebasicconceptstreatedinVolumeI:groups，rings，fields，homomorphisms，ispresup-posed.However，wehavetriedtomakethisaccount'oflinearalgebraindependentofadetailedknowledgeofourfirstvolume.Referencestospecificresultsaregivenoccasionallybutsomeofthefundamentalconceptsneededhavebeentreatedagain.Inshort，itishopedthatthisvolumecanbereadwithcompleteunderstandingbyanystudentwhoismathematicallysufficientlymatureandwhohasafamiliaritywiththestandardnotionsofmodernalgebra.

【目录】

CHAPTERI:FINITEDIMENSIONALVECTORSPACES
SECTION
1.Abstractvectorspaces
2.Rightvectorspaces
3.o-modules
4.Lineardependence
5.Invarianceofdimensionality
6.Basesandmatrices
7.Applicationstomatrixtheory
8.Rankofasetofvectors
9.Factorspaces
10.Algebraofsubspaces
11.Independentsubspaces,directsums

CHAPTERII:LINEARTRANSFORMATIONS
1.Definitionandexamples
2.Compositionsoflineartransformations
3.Thematrixofalineartransformation
4.Compositionsofmatrices
5.Changeofbasis.Equivalenceandsimilarityofmatrices
6.Rankspaceandnullspaceofalineartransformation
7.Systemsoflinearequations
8.Lineartransformationsinrightvectorspaces
9.Linearfunctions
10.Dualitybetweenafinitedimensionalspaceandits.conjugatespace
11.Transposeofalineartransformation
12.Matricesofthetranspose
13.Projections

CHAPTERIII:THETHEORYOFASINGLELINEARTRANSFORMATION
1.Theminimumpolynomialofalineartransformation
2.Cyclicsubspaces
3.Existenceofavectorwhoseorderistheminimumpolynomial
4.Cycliclineartransformations
5.Themoduledet:ermiriedbyalineartransformation
6.Finitelygeneratedo-modules,o,aprincipalidealdomain
7.Normalizationofthegeneratorsof;andof
8.Equivalenceofmatriceswithelementsinaprincipalidealdomain
9.Structureoffinitelygeneratedo-modules
10.Invarjancetheorems
11.Decompositionofavectorspacerelativetoalineartrans-formation
12.Thecharacteristicandminimumpolynomials
13.DirectproofofTheorem13
14.Formalpropertiesofthetraceandthecharacteristicpoly-nomial
15.Theringofo-endomorphismsofacyclico-module
16.Determinationoftheringofo-endomorphismsofafinitelygeneratedo-module,oprincipal
17.Thelineartransformationswhichcommutewithagivenlin-eartransformation
18.Thecenterofthering

CHAPTERⅣ:SETSOFLINEARTRANSFORMATIONS
1.Invariantsubspaces
2.Inducedlineartransformations
3.Compositionseries
4.Decomposability
5.Completereducibility
6.Relationtothetheoryofoperatorgroupsandthetheoryofmodules
7.Reducibility,decomposability,completereducibilityforasinglelineartransformation
8.Theprimarycomponentsofaspacerelativetoalineartrans-formation
9.Setsofcommutativelineartransformations

CHAPTERⅤ:BILINEARFORMS
1.Bilinearforms
2.Matricesofabilinearform
……

CHAPTERVI:EUCLIDEANANDUNITARYSPACES
CHAPTERⅦ:PRODUCTSOFVECTORSPApES
CHAPTERⅧ:THERINGOFLINEARTRANSFORMATIONS
CHAPTERIX:INFINITEDIMENSIONALVECTORSPACES
Index