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Exterior Algebras
Elementary Tribute to Grassmann's Ideas
Provides the theoretical basis for exterior computations, first addresses the important question of constructing (pseudo)-Euclidian Grassmmann's algebras
Vincent Pavan (Author)
9781785482373, Elsevier Science
Hardback, published 23 May 2017
208 pages
22.9 x 15.1 x 2 cm, 0.38 kg
"This book covers a lot of ground and will be welcomed by specialists. Although the author describes this book as an ‘elementary’ tribute to Grassmann’s ideas, it is not an easy book to read. On the other hand, the proofs are complete and the discussions are comprehensive." --Zentralblatt MATH 1377 "It is marvelous that Pavan has undertaken to present such a thorough treatment of Grassmann’s work, both because of its intrinsic elegance and because of its utility across mathematics, especially in differential geometry. It is a solid work of scholarship as well as pedagogy." --MAA Reviews
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. 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
