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Additional Physical Format: | Online version: Dickson, Leonard E. (Leonard Eugene), 1874- Algebraic invariants. New York, J. Wiley & Sons; [etc.] 1914 (OCoLC)609297574 |
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Material Type: | Internet resource |

Document Type: | Book, Internet Resource |

All Authors / Contributors: |
Leonard E Dickson |

OCLC Number: | 1014826 |

Description: | x, 100 pages : diagrams ; 24 cm. |

Contents: | pt I. Illustrations, geometrical interpretations and applications of invariants and covariants. Illustrations form plane analytics -- Projective transformations -- Homogeneous coördinates of a point in a line -- Examples of invariants -- Examples of covariants -- Forms and their classification -- Definition of invariants and covariants -- Invariants of covariants -- Canonical form of a binary cubic: solution of cubic equations -- Covariants of covariants -- Intermediate invariants and covariants -- Homogeneous coördinates of points in a plane -- Properties of the Hessian -- Inflexion points and invariants of a cubic curve -- pt. II. Theory of invariants in non-symbolic notation. Homogeneity of invariants -- Weight of an invariant of a binary form -- Weight of an invariant of an system of forms -- Products of linear transformations -- Generators of all binary linear transformations -- Annihilator of an invariant of a binary form -- Homogeneity of covariants -- Weight of a covariant of a binary form -- Annihilators of covariants -- Alternants -- Seminivariants as leaders of binary covariants -- Number of linearly independent seminvariants -- Hermite's law of reciprocity -- Fundamental system of covariants -- Canonical form of binary quartic; solution of quartic equations -- Seminvariants in terms of the roots -- Invariants in terms of the roots -- Covariants in terms of the roots -- Covariant with a given leader -- Differential operators producing covariants -- pt. III. Symbolic notation. The notation and its immediate consequences -- Covariants as functions of two symbolic types -- Reduction to problem on invariants -- Hilbert's theorem on a set of forms -- Finiteness of a fundamental system of invariants -- Finiteness of Syzygies -- Transvectants -- Binary forms apolar to given forms -- Rational plane cubic curves -- Rational space quartic curves -- Fundamental system of covariants of linear forms; of a quadratic form; exercises -- Theorems on transvectants; convolution -- Irreducible covariants found by induction -- Fundamental system for a binary cubic -- Results and references on higher binary forms -- Hermite's law of reciprocity symbolically -- Ternary form in symbolic notation --Concomitants of ternary forms -- Quaternary forms. |

Series Title: | Mathematical monographs (New York, N.Y.), no. 14. |

Responsibility: | by Leonard Eugene Dickson. |

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