图文详情
- ISBN:9787510061523
- 装帧:一般胶版纸
- 册数:暂无
- 重量:暂无
- 开本:32开
- 页数:93
- 出版时间:2013-10-01
- 条形码:9787510061523 ; 978-7-5100-6152-3
本书特色
《抽象代数讲义》是一套久负盛名的三卷集教材,是作者雅格布斯根据他在霍普金斯大学和耶鲁大学讲课时的讲义编写而成的,后又成为作者《基本代数学》一书的蓝本。第1卷介绍了群、环、域、同构等抽象代数的重要的基本概念和抽象代数的基本性质。《抽象代数讲义(第2卷》主要涉及线性代数理论,着重论述了向量空间理论。
内容简介
《抽象代数讲义(第2卷)(英文)》是一套久负盛名的三卷集教材,是作者根据他在霍普金斯大学和耶鲁大学讲课时的讲义编写而成的,后又成为作者这一书的蓝本。第1卷介绍了群、环、域、同构等抽象代数的重要的基本概念和抽象代数的基本性质。第2卷主要涉及线性代数理论,着重论述了向量空间理论。第3卷介绍域理论和伽罗瓦理论,讨论了域的代数结构和域的赋值理论。
目录
CHAPTER I: FINITE DIMENSIONAL VECTOR SPACES
SECTION
1. Abstract vector spaces
2. Right vector spaces
3. o-modules'.
4. Linear dependence
5. Invariance of dimensionality
6. Bases and matrices
7. Applications to matrix theory
8. Rank of a set of vectors
9. Factor spaces
I0. Algebra of subspaces
11. Independent subspaces, direct sums . . .
CHAPTER II: LINEAR TRANSFORMATIONS
1. Definition and examples
CHAPTER I: FINITE DIMENSIONAL VECTOR SPACES
SECTION
1. Abstract vector spaces
2. Right vector spaces
3. o-modules'.
4. Linear dependence
5. Invariance of dimensionality
6. Bases and matrices
7. Applications to matrix theory
8. Rank of a set of vectors
9. Factor spaces
I0. Algebra of subspaces
11. Independent subspaces, direct sums . . .
CHAPTER II: LINEAR TRANSFORMATIONS
1. Definition and examples
2. Compositions of linear transformations
3. The matrix of a linear transformation
4. Compositions of matrices
5. Change of basis. Equivalence and similarity of matrices
6. Rank space and null space of a linear transformation
7. Systems of linear equations
8. Linear transformations in right vector spaces
9. Linear functions
10. Duality between a finite dimensional space and its conjugate
space
11. Transpose of a linear transformation
12. Matrices of the transpose
13. Projections
CHAPTER III: THE THEORY OF A SINGLE LINEAR TRANSFORMATION
1. The minimum polynomial of a linear transformation
2. Cyclic subspaces
……
SECTION
1. Abstract vector spaces
2. Right vector spaces
3. o-modules'.
4. Linear dependence
5. Invariance of dimensionality
6. Bases and matrices
7. Applications to matrix theory
8. Rank of a set of vectors
9. Factor spaces
I0. Algebra of subspaces
11. Independent subspaces, direct sums . . .
CHAPTER II: LINEAR TRANSFORMATIONS
1. Definition and examples
CHAPTER I: FINITE DIMENSIONAL VECTOR SPACES
SECTION
1. Abstract vector spaces
2. Right vector spaces
3. o-modules'.
4. Linear dependence
5. Invariance of dimensionality
6. Bases and matrices
7. Applications to matrix theory
8. Rank of a set of vectors
9. Factor spaces
I0. Algebra of subspaces
11. Independent subspaces, direct sums . . .
CHAPTER II: LINEAR TRANSFORMATIONS
1. Definition and examples
2. Compositions of linear transformations
3. The matrix of a linear transformation
4. Compositions of matrices
5. Change of basis. Equivalence and similarity of matrices
6. Rank space and null space of a linear transformation
7. Systems of linear equations
8. Linear transformations in right vector spaces
9. Linear functions
10. Duality between a finite dimensional space and its conjugate
space
11. Transpose of a linear transformation
12. Matrices of the transpose
13. Projections
CHAPTER III: THE THEORY OF A SINGLE LINEAR TRANSFORMATION
1. The minimum polynomial of a linear transformation
2. Cyclic subspaces
……
展开全部
节选
《抽象代数讲义》是一套久负盛名的三卷集教材,是作者雅格布斯根据他在霍普金斯大学和耶鲁大学讲课时的讲义编写而成的,后又成为作者《基本代数学》一书的蓝本。第1卷介绍了群、环、域、同构等抽象代数的重要的基本概念和抽象代数的基本性质。《抽象代数讲义(第2卷》主要涉及线性代数理论,着重论述了向量空间理论。
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