Exterior Algebras

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.

Autorentext

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.

Klappentext

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.

Inhalt

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. 2E Algebra