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- 208 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
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About This Book
Exterior Algebras: Elementary Tribute to Grassmann's Ideas provides the theoretical basis for exterior computations. It first addresses the important question of constructing (pseudo)-Euclidian Grassmmann's algebras. Then, it shows how the latter can be used to treat a few basic, though significant, questions of linear algebra, such as co-linearity, determinant calculus, linear systems analyzing, volumes computations, invariant endomorphism considerations, skew-symmetric operator studies and decompositions, and Hodge conjugation, amongst others.
- Presents a self-contained guide that does not require any specific algebraic background
- Includes numerous examples and direct applications that are suited for beginners
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Topic
MatematicaSubtopic
Algebra1
Reminders on Linear Algebra
Abstract
In this section, we recall only the essential definitions and results of linear algebra which are useful for the rest of the book. We shall usually choose to consider the case of infinite dimension, which will be indispensable from the perspective of construction of exterior algebras in the next chapter. Most demonstrations are omitted to the extent that they are either quite simple or inappropriate for a chapter without the aim of repeating a detailed course on algebra.
Keywords
Algebraic duality; Bilinear maps; Injections; Linear Algebra; Linear spaces; Partition and equivalence relation; Permutations; Quotient linear space; Skew-symmetric multi-linear maps; Surjections
In this section, we recall only the essential definitions and results of linear algebra which are useful for the rest of the book. We shall usually choose to consider the case of infinite dimension, which will be indispensable from the perspective of construction of exterior algebras in the next chapter. Most demonstrations are omitted to the extent that they are either quite simple or inappropriate for a chapter without t...
Table of contents
- Cover
- Title page
- Table of Contents
- Copyright
- Preface
- Introduction
- 1: Reminders on Linear Algebra
- 2: Construction of Exterior Algebras
- 3: Exterior Product Symbol
- 4: Bases of Exterior Algebras
- 5: Determinants
- 6: Pseudo-dot Products
- 7: Pseudo-Euclidean Algebras
- 8: Divisibility and Decomposability
- 9: H-conjugation and Regressive Product
- 10: Endomorphisms of Exterior Algebras
- 11: Λ2E Algebra
- Bibliography
- Index