This chapter presents quadratic mappings in general, and quadratic forms in particular. It affords many results that will be useful in the next chapter devoted to Clifford algebras; for instance the concept of “hyperbolic space” presented in 2.5 and the theorems of orthogonal decomposition expounded in 2.6 will be especially helpful in 3.7, where their effectiveness also depends on an insightful use of localization and globalization. Besides, the concept of “hyperbolic space” is also essential in the last Sections 2.7 and 2.8 devoted to Witt rings.
KeywordsQuadratic Form Quadratic Mapping Hyperbolic Space Projective Module Symmetric Bilinear Form
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