矩阵空间的保持问题

张显, 唐孝敏, 曹重光, 著

出版社：科学出版社

年代：2007

定价：68.0

书籍简介:

本书介绍矩阵论的一个研究领域——保持问题。主要内容包括最小秩保持、秩加性保持、秩等价保持、平方零保持、k-幂保持、k-幂等保持、矩阵（广义）逆保持、对合保持、伴随保持、乘积保持等。

书籍目录:

Preface

Notation

Chapter1Introductiontopreserverproblems

1.1Definitions

1.2Typicalcategoriesofpreserverproblems

1.3TechniquesofPreserverProblems

1.4Organization

Chapter2Preserversofthesmallestnonzerorank

2.1Additiverank-1preserversbetweenspacesofrectangularmatrices

2.2Additiverank-1preserversbetweenspacesofsymmetricmatrices

2.3Additiverank-1preserversbetweenspacesofHermitianmatrices

2.4Additiverank-1preserversfromaspaceoftriangularmatricestoaspaceofsquarematrices

2.5Additiverank-2preserversbetweenspacesofalternatematrices

2.6Invertiblelinearrank-1preserversonspacesoftracezeromatrices

2.7Invertibility(characteristicpolynomial,determinant)preservers

2.8RemarksonChapter2

Chapter3Additiverank-additivitypreserversandapplications

3.1Additiverank-additivitypreserversonspacesofrectangularmatrices

3.2Additiverank-additivitypreserversonspacesofsymmetricmatrices

3.3Additiverank-additivitypreserversonspacesofHermitianmatrices

3.4Additiverank-additivitypreserversonspacesofalternatematrices

3.5Applicationsofadditiverank-additivitypreservers

3.6RemarksonChapter3

Chapter4Additivepreserversofrankequivalenceandapplications

4.1Mainresults

4.2Proofsofmainresults

4.3RemarksonChapter4

Chapter5Linearsquare-zeropreserversonspacesofsquarematrices

5.1Mainresults

5.2Proofsofmainresults

5.3RemarksonChapter5

Chapter6Preserversofk-power/k-potent

6.1Additivepreserversofidempotencebetweenspacesofsquarematrices

6.2Injectiveadditivepreserversofidempotenceonspacesoftriangularmatrices

6.3Linearpreserversofidempotencebetweenspacesofsymmetricmatrices

6.4Severalproblemsrelatedtok-powerandk-potentpreservers

6.5Preserversofk-power

6.6Preserversofk-potentmatrices

6.7Jordanhomomorphismsbetweenofringsofsquarematrices

6.8Preserversofidempotentrelation

6.9RemarksonChapter6

Chapter7Preserversofinversesofmatrices

7.1Linearinversepreserversbetweenspacesofmatrices

7.2Additiveinversepreserversbetweenspacesofmatrices

7.3RemarksonChapter7

Chapter8Preserversofgeneralizedinversesofmatrices

8.1AdditivepreserversofM-Pinversesofmatricesoverfields

8.2Additivepreserversof{1,2}-inversesofmatricesoverfields

8.3Additivepreserversofgroupinversesofmatricesoverfields

8.4StronglinearpreserversofMoore-Penroseinversesofmatricesoverthetwo-elementBooleanalgebra

8.5CovariantoperatorpairsonM-PInversesofmatricesbetweenrealfinitedimensionaldivisionalgebras

8.6RemarksonChapter8

Chapter9Linearpreserversofinvolutorymatrices

9.1Mainresults

9.2Proofsofmainresults

9.3RemarksonChapter9

Chapter10Additiveadjointpreservers

10.1Mainresults

10.2Proofsofmainresults

10.3RemarksonChapter10

Chapter11Preserversofmultiplication

11.1Homomorphismsfromonegenerallineargrouptoanother

11.2Homomorphismsfromamultiplicativematrixsemigrouptoanother

11.3Automorphismsofmultiplicativesemigroupsofuppertriangularmatrices

11.4RemarksonChapter11

AppendixAFittingdecompositionofamatrix

AppendixBCanonicalformofarank-additivematrixpair

AppendixCCanonicalformofamatrixtriple

AppendixDAdjointmatrices

Bibliography

Index

内容摘要:

　　Oneoftheveryactiveresearchareasinmatrixtheoryisthestudyofpreserverproblems,includinglinearpreserverproblems,additivepreserverproblemsandmultiplicativepreserverproblems,whichconcerntheclassificationofmapsonmatricesoroperatorsthatpreservecertainspecialproperties.　　Theaimofthisbookistoprovideanintroductiontocurrentadvancesofpreserverproblemsonmatricesandpresentthebasicmethodsofstudyingpreserverproblems.Inordertoensurethatthecontentisself-contained,wetooksomeconclusionsandtheirproofsfromotherbooksorpapers,whichwillbeconvenienttothereaders.Itisalsointendedtoofferacollectioaofreferencesonpreserverproblemsonmatrices.Thisbookisespeciallyappropriateforadvancedundergraduatesmajoredinmathematics,andalsointendedforgraduatestudentsandresearchlevelmathematicians.Itishopedthatthebookwillbesuitabeforpostgraduatetouseorasareference.Thereadersarerequiredtofamiliarizewithmatrixmethodsandtocomprehendsomebasicconceptsinalgebra,suchaslinearspace,(semi-)group,(semi-)ring,homomorphism,isomorphism,etc.

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出版地	北京	出版单位	科学出版社
版次	1版	印次	1
定价(元)	68.0	语种	英文
尺寸	24	装帧	精装
页数		印数

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书籍信息归属:

矩阵空间的保持问题是科学出版社于2007.出版的中图分类号为 O151.21 的主题关于矩阵－研究－英文的书籍。