Squares [EBook] / A.R. Rajwade.
Squares [EBook] / A.R. Rajwade.
Many classical and modern results and quadratic forms are brought together in this book. The treatment is selfcontained 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...
Personal Name(s):  Rajwade, A. R., (author) 

Imprint: 
Cambridge :
Cambridge University Press,
1993

Physical Description: 
1 online resource (xii, 286 pages) 
Note: 
englisch 
ISBN: 
9780511566028 9780521426688 
Series Title: 
London Mathematical Society lecture note series ;
171 
Subject (LOC):  
Full Text 
Table of Contents:
 The theorem of Hurwitz (1898) on the 2, 4, 8identities
 The 2nidentities 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 semidefinite 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 HurwitzRadon (192223)
 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
 ArtinSchreier 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 HasseMinkowski theorem
 Reduction of matrices to canonical forms (for Chapter 10)
 Convex sets (for chaptes 6,7,8,9).