Algebraic Invariants by Leonard E. Dickson - PDF

About this book :-
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 Detail :-
Title: Algebraic Invariants by Leonard E. Dickson - PDF
Publisher: J. Wiley & Sons
Year: 1914
Pages: 122
Type: PDF
Language: English
ISBN-10 #: 1603861750
ISBN-13 #:
License: Public Domain Work
Amazon: Amazon

About Author :-
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.

Book 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

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