《FOUNDATIONS OF THE THEORY OF ALGEBRAIC INVARIANTS》求取 ⇩
| 作者 | G.B.GUREVICH 编者 |
|---|---|
| 出版 | P.NOORDHOFF LTD |
| 参考页数 | 429 ✅ 真实服务 非骗流量 ❤️ |
| 出版时间 | 1964（求助前请核对） 目录预览 |
| ISBN号 | 无 — 违规投诉 / 求助条款 |
| PDF编号 | 813427878（学习资料 勿作它用） |
| 求助格式 | 扫描PDF（若分多册发行，每次仅能受理1册） |
CHAPTER Ⅰ．Geometric introduction1
1The invariants of transformations of Cartesian coordinates1
2 The group of motions13
3 The group of motions and reflections;the principal group16
4 Affine transformations of the plane21
5 Projective transformations of a straight line39
6 Projective transformations of the plane51
7 The reduction of affine invariants to projective invariants and of metric invariants to affine and projective invariants68
8 Multi-dimensional space85
CHAPTER Ⅱ．The foundations of tensor algebra99
9Tensors and operations on tensors99
10 The geometric meaning of tensors;the projective point of view115
11 The geometric meaning of tensors;the affine point of view126
12 Relative tensors and their operations133
CHAPTER Ⅲ．Invariants and concomitants of tensors and their simplest properties139
13Invariants and concomitants of tensors139
14 Examples of invariants and concomitants143
15 The simplest properties of invariants159
CHAPTER Ⅳ．The fundamental theorem of the theory of invariants and its consequences170
16Tensors with constant components170
17 Proof of the fundamental theorem182
18 The symbolic method in invariant theory189
19 Fundamental identities209
20 Invariant processes223
21 Complete systems of invariants235
CHAPTER Ⅴ．Binary forms246
22Linear and quadratic binary forms246
23 Cubic binary forms261
24 Gordan＇s method for finding complete systems of concomitants of binary forms．Gordan-Clebsch series272
25 Binary forms of fourth order285
26 Differential equations for invariants and semi-invariants of binary285
forms294
CHAPTER Ⅵ．Ternary forms．Second order tensors308
27The quadratic ternary form308
28 Geometric interpretations of the simplest concomitants of ternary forms of order r317
29 The quadratic n-ary form326
30 Mixed second order tensors(affinors)338
CHAPTER Ⅶ．Polyvectors353
31Certain general properties of polyvectors353
32 Geometric interpretation of polyvectors．Weitzenbock＇s complex symbolic notation363
33 Condition for divisibility of a polyvector by one or several vectors374
34 The bi-vector381
35 The tri-vector390
Answers and hints to exereises396
Literature418
Index419
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