抽象代數講義（第2捲）（英文） [Lectures in Abstract Algebra 2] pdf epub mobi txt 電子書 下載 2025

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[德] 雅格布斯（Jacobson N.） 著

齣版社： 世界圖書齣版公司

ISBN：9787510061523

版次：1

商品編碼：11308639

包裝：平裝

外文名稱：Lectures in Abstract Algebra 2

開本：24開

齣版時間：2013-10-01

用紙：膠版紙

頁數：280

正文語種：英文

內容簡介

　　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.

內頁插圖

目錄

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

評分☆☆☆☆☆

作者可以說是至始至終都與這種思想相背離著。《紅樓夢》可以未完，但絕對不可以庸俗！而《紅樓夢》從來是不缺乏結局的，從很大數量的續書中就可以看齣，現在也有不少這樣的好心人，誇大，裝腔，撒謊，煞有其事……目的也隻有一個，那就是結局，這點比百二十迴的“不結而結”可以說是等而下之瞭。而瓊瑤小說影視之所以走紅，通常就是在結局中玩盡一些哭天搶地的把戲，使讀者和著作者一起用無聊消乏無聊，用一切的無聊把一切的無聊送走。

評分☆☆☆☆☆

經典教材，英文版很好

評分☆☆☆☆☆

自摸色哦教育局福伊特咯哇

評分☆☆☆☆☆

大學教授推薦的英文書，正在看，內容目前無法評價。

評分☆☆☆☆☆

知我者謂我心憂我現在在知我者謂我心憂

評分☆☆☆☆☆

評分☆☆☆☆☆

自摸色哦教育局福伊特咯哇

評分☆☆☆☆☆

不錯的書，好好學習天天嚮上

評分☆☆☆☆☆

沒找到basic algebra纔買的，雖然是影印版，但是很清晰。