In Section 6.4 we gave an intuitive introduction to the concept of Grassmann algebra as an associative algebra of dimension constructed from a vector space of dimension . Certain difficulties, particularly those relating to the definition of exterior product, were cleared up by the more formal approach to the subject in Section 7.1. In this chapter we propose a definition of Grassmann algebra entirely of tensors [1–5]. This presentation has a more ‘concrete’constructive character, and to distinguish it from the previous treatments we will use the term exterior algebra over to describe it from here on.
Contents
- 8.1 r-Vectors and r-forms
- 8.2 Basis representation of r-vectors
- 8.3 Exterior product
- 8.4 Interior product
- 8.5 Oriented vector spaces
- 8.6 The Hodge dual
Concept index
Terms by section. Links lead to the brown underlined definitions in the Chinese reading text.
8.1 r-Vectors and r-forms
8.3 Exterior product
- multivector多重向量
- exterior product外积
- wedge product楔积
- exterior algebra外代数
- graded product分次积
- graded algebra分次代数
- multiform多重形式
8.4 Interior product
8.5 Oriented vector spaces
- volume element体积元
- Levi-Civita symbol列维–奇维塔符号
- orientation定向
- oriented vector space定向向量空间
- generalized delta symbol广义克罗内克符号