Squares
Many classical and modern results and quadratic forms are brought together in this book. The treatment is self-contained and of a totally elementary nature requiring only a basic knowledge of rings, fields, polynomials, and matrices, such that the works of Pfister, Hilbert, Hurwitz and others are ea...
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| Format: | eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
1993
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| Series: | London Mathematical Society lecture note series
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| Subjects: | |
| Online Access: | |
| Collection: | Cambridge Books Online - Collection details see MPG.ReNa |
Table of Contents:
- The theorem of Hurwitz (1898) on the 2, 4, 8-identities
- The 2n-identities and the Stufe of fields : theorems of Pfister and Cassels
- Examples of the Stufe of fields and related topics
- Hilbert's 17th problem and the function fields R(X), Q(X), and R(X, Y)
- Positive semi-definite functions and sums of squares in R(X1,X2, ..., Xn)
- Introduction to Hilbert's theorem (1888) in the ring R[X1,X2, ..., Xn]
- The two proofs of Hilbert's main theorem; Hilbert's own and the other of Choi and Lam
- Theorems of Reznick and of Choi, Lam and Reznick
- Theorems of Choi, Calderon and of Robinson
- The Radon function and the theorem of Hurwitz-Radon (1922-23)
- Introduction to the teory of quadratic forms
- Theory of multiplicative forms and of Pfister forms
- The rational admissibility of the triple (r, s, n) and the Hopf condition
- Some interesting examples of bilinear identities and a theorem of Gabel
- Artin-Schreier theory of formally real fields
- Squares and sums of squares in fields and their extension fields
- Pourchet's theorem that P(Q(X)) = 5 and related results
- Examples of the Stufe and pythagroas number of fields using the Hasse-Minkowski theorem
- Reduction of matrices to canonical forms (for Chapter 10)
- Convex sets (for chaptes 6,7,8,9)