Theory of Algebraic Invariants

Name: Theory of Algebraic Invariants
Price: 9.85 USD
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ISBN: 9780521449038

ISBN-10: 0521449030

ISBN-13: 9780521449038

Edition: 1993

Authors: David Hilbert, Bernd Sturmfels, Reinhard C. Laubenbacher

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Description:

In the summer semester of 1897 David Hilbert (1862-1943) gave an introductory course in Invariant Theory at the University of Gottingen. This book is an English translation of the handwritten notes taken from this course by Hilberts student Sophus Marxen. The year 1897 was the perfect time for Hilbert to present an introduction to invariant theory as his research in the subject had been completed. His famous finiteness theorem had been proved and published in two papers that changed the course of invariant theory dramatically and that laid the foundation for modern commutative algebra. Thus these lectures take into account both the old approach of his predecessors and his newer ideas. This…

Book details

List price: $48.99
Copyright year: 1993
Publisher: Cambridge University Press
Publication date: 11/26/1993
Binding: Paperback
Pages: 208
Size: 6.02" wide x 8.98" long x 0.51" tall
Weight: 0.638



Preface


Introduction



The Elements of Invariant Theory



The forms



The linear transformation



The concept of an invariant



Properties of invariants and covariants



The operation symbols D and D



The smallest system of conditions for the determination of the invariants and covariants



The number of invariants of degree g



The invariants and covariants of degree two and three



Simultaneous invariants and covariants



Covariants of covariants



The invariants and covariants as functions of the roots



The invariants and covariants as functions of the one-sided derivatives



The symbolic representation of invariants and covariants



The Theory of Invariant Fields



Proof of the finitenesss of the full invariant system via representation by root differences



A generalizable proof for the finiteness of the full invariant system



The system of invariants I; I1, I2, ..., Ik



The vanishing of the invariants



The ternary nullform



The finiteness of the number of irreducible syzygies and of the syzygy chain



The inflection point problem for plane curves of order three



The generalization of invariant theory



Observations about new types of coordinates