Linear and Bilinear Forms

Garret Sobczyk
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Garret Sobczyk: Universidad de Las Américas, Departamento de Física y Matemáticas

Chapter Chapter 9 in New Foundations in Mathematics, 2013, pp 137-151 from Springer

Abstract: Abstract Geometric algebra is not used in this chapter. The material presented is closely related to the material in Sect. 7.1 but represents a change of viewpoint. Instead of talking about the reciprocal basis of a given basis, we introduce the concept of a dual basis. The relationship between a bilinear and a quadratic form is discussed, and Sylvester’s famous law of inertia is proven. The material lays the foundation for studying geometric algebras of arbitrary signatures in later chapters.

Keywords: Symmetric Bilinear Form; Geometric Algebra; Standard Dual Basis; Reciprocal Basis; Quadratic Form (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-0-8176-8385-6_9

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