Hermitian Inner Product Spaces

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

Chapter Chapter 10 in New Foundations in Mathematics, 2013, pp 153-179 from Springer

Abstract: Abstract In the last chapter, we discovered that the positive definite quadratic form (3.28) used to define the inner product of the Euclidean space $${\mathbb{R}}^{n}$$ , and the corresponding geometric algebra $${\mathbb{G}}_{n} = \mathbb{G}({\mathbb{R}}^{n})$$ , is only one of the many possible quadratic forms. We now introduce the pseudo-Euclidean space $${\mathbb{R}}^{p,q}$$ of a general indefinite quadratic form $$q(\mathbf{x})$$ and the corresponding geometric algebra $${\mathbb{G}}_{p,q} = \mathbb{G}({\mathbb{R}}^{p,q})$$ .

Keywords: Geometric Algebra; Principal Correlation; Complex Linear Operator; Orthogonal Hermite; Diagonal Gram (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-8385-6_10

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DOI: 10.1007/978-0-8176-8385-6_10

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