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抽象代數(shù)講義-第2卷 版權(quán)信息
- ISBN：9787510061523
- 條形碼：9787510061523 ; 978-7-5100-6152-3
- 裝幀：一般膠版紙
- 冊數(shù)：暫無
- 重量：暫無
- 所屬分類：>>
抽象代數(shù)講義-第2卷 本書特色
《抽象代數(shù)講義》是一套久負盛名的三卷集教材,是作者雅格布斯根據(jù)他在霍普金斯大學和耶魯大學講課時的講義編寫而成的,后又成為作者《基本代數(shù)學》一書的藍本。第1卷介紹了群、環(huán)、域、同構(gòu)等抽象代數(shù)的重要的基本概念和抽象代數(shù)的基本性質(zhì)。《抽象代數(shù)講義(第2卷》主要涉及線性代數(shù)理論,著重論述了向量空間理論。
抽象代數(shù)講義-第2卷 內(nèi)容簡介
《抽象代數(shù)講義(第2卷)(英文)》是一套久負盛名的三卷集教材，是作者根據(jù)他在霍普金斯大學和耶魯大學講課時的講義編寫而成的，后又成為作者這一書的藍本。第1卷介紹了群、環(huán)、域、同構(gòu)等抽象代數(shù)的重要的基本概念和抽象代數(shù)的基本性質(zhì)。第2卷主要涉及線性代數(shù)理論，著重論述了向量空間理論。第3卷介紹域理論和伽羅瓦理論，討論了域的代數(shù)結(jié)構(gòu)和域的賦值理論。
抽象代數(shù)講義-第2卷 目錄
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
……
展開全部
抽象代數(shù)講義-第2卷 節(jié)選
《抽象代數(shù)講義》是一套久負盛名的三卷集教材,是作者雅格布斯根據(jù)他在霍普金斯大學和耶魯大學講課時的講義編寫而成的,后又成為作者《基本代數(shù)學》一書的藍本。第1卷介紹了群、環(huán)、域、同構(gòu)等抽象代數(shù)的重要的基本概念和抽象代數(shù)的基本性質(zhì)。《抽象代數(shù)講義(第2卷》主要涉及線性代數(shù)理論,著重論述了向量空間理論。
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