Algebraic Invariants by Leonard E. Dickson
Algebraic Invariants - Table of Contents
Part-I Illustrations, Geometrical Interpretations and Applications of Invariants and Covariants
1. Illustrations from Plane Analytics
2. Projective Transformations
3. Homogeneous Coordinates of a Point in a Line
4. Examples of Invariants
5. Examples of Covariants
6. Forms and Their Classification
7. Definition of Invariants and Covariants
8. Invariants of Covariants
9. Canonical Form of a Binary Cubic: Solution of Cubic Equations
10. Covariants of Covariants
11. Intermediate Invariants and Covariants
12. Homogeneous Coordinates of Points in a Plane
13. Properties of the Hessian
14. Inflexion Points and Invariants of a Cubic Curve
Part-II Theory of Invariants in Non-symbolic Notation
15. Homogeneity of Invariants
16. Weight of an Invariant of a Binary Form
17. Weight of an Invariant of any System of Forms
18. Products of Linear Transformations
19. Generators of all Binary Linear Transformations
20. Annihilator of an Invariant of a Binary Form
21. Homogeneity of Covariants
22. Weight of a Covariant of a Binary Form
23. Annihilators of Covariants
24. Alternants
25. Seminvariants as Leaders of Binary Covariants
26. Number of Linearly Independent Seminvariants
27. Hermite's Law of Reciprocity
28-3L Fundamental System of Covariants
32, 33. Canonical Form of Binary Quartic; Solution of Quartic Equations.
34. Seminvariants in Terms of the Roots
35. Invariants in Terms of the Roots
36. Covariants in Terms of the Roots
37. Covariant with a Given Leader
38. Differential Operators Producing Covariants
Part-III Symbolic Notation
39-41. The Notation and its Immediate Consequences
42-45. Covariants as Functions of Two Symbolic Types
46. Problem of Finiteness of Covariants
47. Reduction to Problem on Invariants
48. Hubert's Theorem on a Set of Forms
49, 50. Finiteness of a Fundamental System ot Invariants
51 . Finiteness of Syzygies
52. Transvectants
53, 54. Binary Forms Apolar to Given Forms
55, 56. Rational Plane Cubic Curves
57. Rational Space Quartic Curves
58, 59. Fundamental System of Covariants of Linear Forms; of a Quadratic
60. Theorems on Transvectants; Convolution
61. Irreducible Covariants Found by Induction
62. Fundamental System for a Binary Cubic
63. Results and References on Higher Binary Forms
64. Hermite's Law of Reciprocity Symbolically
65. Ternary Form in Symbolic Notation
66, 67. Concomitants of Ternary Forms
68. Quaternary Forms
What You Will Learn in Algebraic Invariants
This monograph offering one of the early systematic treatments of invariant theory. This introduction to the classical theory of invariants of algebraic forms is divided into three parts. The first uses geometric examples (like conics and cubics) to illustrate invariants and covariants; the second lays out the algebraic foundations—such as homogeneity and annihilators—for binary forms; and the third introduces the classical symbolic notation of Aronhold and Clebsch.
The notation is first explained at length for a simple case; Hkewise the fundamental theorem on the types of symbolic factors of a term of a covariant of binary forms is first proved for a simple example by the method later used for the general theorem.
Book Details & Specifications
Title:
Algebraic Invariants by Leonard E. Dickson
Publisher:
J. Wiley & Sons
Year:
1914
Pages:
122
Type:
PDF
Language:
English
ISBN-10 #:
1603861750
ISBN-13 #:
License:
Public Domain Work
Amazon:
Amazon
About the Author: Leonard Eugene Dickson
The author Leonard Eugene Dickson
(1874–1954) was a leading American algebraist and one of the first U.S. researchers to advance abstract algebra, particularly in finite fields, classical groups, and invariant theory.
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