Linear and Bilinear Forms

doi:https://doi.org/10.1007/978-0-8176-8385-6_9

Linear and Bilinear Forms

Garret Sobczyk-2012-09-19-Birkhäuser Boston eBooks

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TL;DRAbstract

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.

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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

Basis (linear algebra)ReciprocalBilinear interpolationBilinear formAlgebra over a fieldMathematicsPure mathematicsQuadratic equation

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