代數分析

《代數分析》是2015年哈爾濱工業大學出版社出版的圖書。本書語言簡潔易懂，適用於本科及研究生參考閱讀。

基本介紹

• 書名：代數分析
• 作者：[英] 盧瑟福
• 出版社：哈爾濱工業大學出版社
• ISBN：9787560354583

內容簡介

《代換分析（英文版）》講述了對稱群的初步觀點，主要有導數的計算、楊氏公式、基偶數導數，表的計算、正交和自然表示法，不變數二次方程、矩陣、群的特性，代換方程等內容。《代換分析（英文版）》語言簡潔易懂，適用於本科及研究生參考閱讀。

圖書目錄

目錄

Chapter Ⅰ THE CALCUIUS OF PERMUTATIONS

1 Permutations

2 The Symmetric Group fn

3 Cycles and Transpositions

4 Odd and Even Permutations

5 Classes of Permutations

7 The Positive and Negative Symmetric Groups on r Letters

Chapter Ⅱ THE CALCULUS OF TABIEAUX

1 Shapes and Tableaux

2 The Substitutional Expressions P and N

3 The Product PrNs

4 The Expressions E

5 von Neumann's Theorem

6 Young's Formula

7 Tableaux of Different Shapes

Chapter Ⅲ THE SEMI-NORMAL REPRESENTATION

1 Standard Tableaux

2 The Evaluation of fa

3 The Semi-normal Units e

4 Certain Fundamental Formulae

5 The Irreducible Semi-normal Representations of fn

6 Expressions which do not Involve the Last Letter

7 The Semi-normal Matrix for E

8 The Matrices U

9 The Matrices U

Chapter Ⅳ THE ORTHOGONAL AND NATURAL REPRESENTATIONS

1 Equivalent Representations

2 The Invariant Quadratic

3 The Tableau Function

4 The Orthogonal Representation

5 The Matrix

6 The Natural Representation

7 Expressions for the Units g

8 Equivalence of the Natural and Semi-normal Representations

Chapter Ⅴ GROUP CHARACTERS

1 The Expressions Cα

2 The Expressions Tα

3 The Relations between the Expressions Tκ and Cκ

4 The Group Characters of fn

5 The Evaluation of the Group Characters

6 Reduction Formulae

7 Littlewood's Theorem

Chapter Ⅵ SUBSTITUTIONAL EQUATIONS

1 Minimum Functions

2 The Master Idempotent

3 The Substitutional Properties of Functions

4 The Number of Independent Solutions of LX = 0

5 The Solution of the Equation LX = 0

6 Functions which are Invariant under a Group of Substitutional Expressions

7 Some Special Cases

8 The Equation LX = R

Appendix TABLES FOR THE CASE n = 3

Bibliography

Index