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Algebra --- Bilinear forms --- Algèbre. --- Formes bilinéaires.

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The specialization theory of quadratic and symmetric bilinear forms over fields and the subsequent generic splitting theory of quadratic forms were invented by the author in the mid-1970's. They came to fruition in the ensuing decades and have become an integral part of the geometric methods in quadratic form theory. This book comprehensively covers the specialization and generic splitting theories. These theories, originally developed mainly for fields of characteristic different from 2, are explored here without this restriction. In this book, a quadratic form φ over a field of characteristic 2 is allowed to have a big quasilinear part QL(φ) (defined as the restriction of φ to the radical of the bilinear form associated to φ), while in most of the literature QL(φ) is assumed to have dimension at most 1. Of course, in nature, quadratic forms with a big quasilinear part abound. In addition to chapters on specialization theory, generic splitting theory and their applications, the book's final chapter contains research never before published on specialization with respect to quadratic places and will provide the reader with a glimpse towards the future.

Algebraic fields. --- Bilinear forms. --- Forms, Quadratic. --- Forms, Quadratic --- Bilinear forms --- Algebraic fields --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Algebra. --- Mathematics. --- Math --- Science --- Mathematical analysis

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Algebra --- Bilinear forms --- Algèbre. --- Formes bilinéaires. --- Algèbre linéaire. --- Algebras, Linear --- Hilbert, Espaces de --- Hilbert space

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Algebra. --- Bilinear forms --- Algèbre --- Formes bilinéaires. --- Algebre lineaire --- Equations algebriques --- Determinants --- Algebre lineaire --- Equations algebriques --- Determinants

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Forms, Quadratic --- Bilinear forms --- Group theory --- #WWIS:d.d. Prof. L. Bouckaert/BOUC --- #KOPO:Prof. R. Holvoet --- 512.64 --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Quadratic forms --- Diophantine analysis --- Forms, Binary --- Number theory --- Forms, Bilinear --- Forms (Mathematics) --- Linear and multilinear algebra. Matrix theory --- Bilinear forms. --- Forms, Quadratic. --- Group theory. --- 512.64 Linear and multilinear algebra. Matrix theory