Elementary Tribute to Grassmann's Ideas
Publication Date: May 2017 Hardback 208 pp.
Exterior algebras have two key characteristics: they are relatively unknown and essential to linear algebra. Since being theorized by Grassmann in 1844, they have remained tragically forgotten.
This book presents the construction and use of exterior algebra calculations in an elementary and progressive manner. Aimed at students, teachers as well as other users of algebraic calculations – physicians, computer scientists or mathematicians – the author shows how the construction of exterior products not only allows us to simplify classic algebra problems, but also to construct a framework of considerations on antisymmetry.
From the re-writing of common properties of factors and considerations on the volumes of polytopes, to the inversion of operators and the Hodge conjecture, this book is a modest and respectful tribute, aimed at spreading Grassman’s ideas.
1. Reminders on Linear Algebra.
2. Construction of Exterior Algebras.
3. Exterior Product Symbol.
4. Bases of Exterior Algebras.
6. Pseudo-dot Products.
7. Pseudo-Euclidean Algebras.
8. Divisibility and Decomposability.
9. H-conjugation and Regressive Product.
10. Endomorphisms of Exterior Algebras.
11. A2E Algebra.
About the Authors
Vincent Pavan is a lecturer and researcher in the Polytech department at Aix-Marseille University in France. His research focuses on kinetic theory and the Boltzmann equation.