抽象代数讲义（第2卷）（英文） [Lectures in Abstract Algebra 2] epub pdf mobi txt 电子书 下载 2024

抽象代数讲义（第2卷）（英文） [Lectures in Abstract Algebra 2] epub pdf mobi txt 电子书 下载 2024

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抽象代数讲义（第2卷）（英文） [Lectures in Abstract Algebra 2] epub pdf mobi txt 电子书 下载 2024

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内容简介

　　The present volume is the second in the author's series of three dealing with abstract algebra. For an understanding of this volume a certain familiarity with the basic concepts treated in Volume I: groups， rings， fields， homomorphisms， is presup- posed. However， we have tried to make this account' of linear algebra independent of a detailed knowledge of our first volume. References to specific results are given occasionally but some of the fundamental concepts needed have been treated again. In short， it is hoped that this volume can be read with complete understanding by any student who is mathematically sufficiently mature and who has a familiarity with the standard notions of modern algebra.

内页插图

目录

CHAPTER I: FINITE DIMENSIONAL VECTOR SPACES
S ECTION
1. Abstract vector spaces
2. Rightvectorspaces
3. o-modules
4. Linear dependence
5. Invariance of dimensionality
6. Bases and matrices
7. Applications to matrix theory
8. Rank ofa set ofvectors
9. Factor spaces
10. Algebra ofsubspaces
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 ofmatrices
5. Change of basis. Equivalence and similarity of matrices
6. Rank space and null space of a linear transformation
7. Systems oflinear 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. Cyclicsubspaces
3. Existence of a vector whose order is the minimum polynomial
4. Cyclic linear transformations
5. The module det:ermiried by a linear transformation
6. Finitely generated o-modules, o, a principal ideal domain
7. Normalization of the generators of; and of
8. Equivalence of matrices with elements in a principal ideal domain
9. Structure of finitely generated o-modules
10. Invarjance theorems
11. Decomposition of a vector space relative to a linear trans- formation
12. The characteristic and minimum polynomials
13. Direct proof of Theorem 13
14. Formal properties of the trace and the characteristic poly- nomial
15. The ring of o-endomorphisms of a cyclic o-module
16. Determination of the ring of o-endomorphisms of a finitely generated o-module, o principal
17. The linear transformations which commute with a given lin- ear transformation
18. The center of the ring

CHAPTER Ⅳ: SETS OF LINEAR TRANSFORMATIONS
1. Invariant subspaces
2. Induced linear transformations
3. Composition series
4. Decomposability
5. Complete reducibility
6. Relation to the theory of operator groups and the theory of modules
7. Reducibility, decomposability, complete reducibility for a single linear transformation
8. The primary components of a space relative to a linear trans- formation
9. Sets of commutative linear transformations

CHAPTER Ⅴ: BILINEAR FORMS
1. Bilinear forms
2. Matrices of a bilinear form
……

CHAPTER VI: EUCLIDEAN AND UNITARY SPACES
CHAPTER Ⅶ: PRODUCTS OF VECTOR SPApES
CHAPTER Ⅷ: THE RING OF LINEAR TRANSFORMATIONS
CHAPTER IX: INFINITE DIMENSIONAL VECTOR SPACES
Index

前言/序言

抽象代数讲义（第2卷）（英文） [Lectures in Abstract Algebra 2] epub pdf mobi txt 电子书 下载 2024

抽象代数讲义（第2卷）（英文） [Lectures in Abstract Algebra 2] 下载 epub mobi pdf txt 电子书 2024

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一、不同人生阶段、不同认知水平对应的“有效读书”标准不一样

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The present Vrolume completes the series of texts on algebra which the author began more than ten years ago. The account of field theory and Galois theory which we girre here is based on the notions and results of general algebra which appear in our first volume and on the more elementary parts of the second volume， dealing with linear algebra. The level of the present work .is roughly the same as that of Volume II.

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好书，值得阅读。要好好学习，天天向上啊！

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很棒的书啊，我很喜欢的呢

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作者可以说是至始至终都与这种思想相背离着。《红楼梦》可以未完，但绝对不可以庸俗！而《红楼梦》从来是不缺乏结局的，从很大数量的续书中就可以看出，现在也有不少这样的好心人，夸大，装腔，撒谎，煞有其事……目的也只有一个，那就是结局，这点比百二十回的“不结而结”可以说是等而下之了。而琼瑶小说影视之所以走红，通常就是在结局中玩尽一些哭天抢地的把戏，使读者和着作者一起用无聊消乏无聊，用一切的无聊把一切的无聊送走。

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三大本，够我啃一阵子的，锻炼毅力啊

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不错1234567890

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不错的书，好好学习天天向上

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