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.
1. Introduction - p. xiii 2. 1: Reminders on Linear Algebra - p. 1 3. 2: Construction of Exterior Algebras - p. 19 4. 3: Exterior Product Symbol - p. 31 5. 4: Bases of Exterior Algebras - p. 45 6. 5: Determinants - p. 55 7. 6: Pseudo-dot Products - p. 77 8. 7: Pseudo-Euclidean Algebras - p. 95 9. 8: Divisibility and Decomposability - p. 111 10. 9: H-conjugation and Regressive Product - p. 121 11. 10: Endomorphisms of Exterior Algebras - p. 141 12. 11: Λ2E Algebra - p. 165 13. Bibliography - p. 189 14. Index - p. 191
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.
1. Introduction - p. xiii 2. 1: Reminders on Linear Algebra - p. 1 3. 2: Construction of Exterior Algebras - p. 19 4. 3: Exterior Product Symbol - p. 31 5. 4: Bases of Exterior Algebras - p. 45 6. 5: Determinants - p. 55 7. 6: Pseudo-dot Products - p. 77 8. 7: Pseudo-Euclidean Algebras - p. 95 9. 8: Divisibility and Decomposability - p. 111 10. 9: H-conjugation and Regressive Product - p. 121 11. 10: Endomorphisms of Exterior Algebras - p. 141 12. 11: Λ2E Algebra - p. 165 13. Bibliography - p. 189 14. Index - p. 191
