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Exterior Algebras - 1st Edition - ISBN: 9781785482373, 9780081023488

Exterior Algebras

1st Edition

Elementary Tribute to Grassmann's Ideas

Author: Vincent Pavan
Hardcover ISBN: 9781785482373
eBook ISBN: 9780081023488
Imprint: ISTE Press - Elsevier
Published Date: 23rd May 2017
Page Count: 208
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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.

Key Features

  • Presents a self-contained guide that does not require any specific algebraic background
  • Includes numerous examples and direct applications that are suited for beginners


Undergraduate students, both in theoretical or applied science. They may belong to the field of Mathematics, Computer Science or Physics as well. However the monograph can also hit confirmed researchers who want to get familiar with algebraic techniques they are not used to computing with. Finally, in France, such a topic can also interest people preparing for secondary teaching positions and students preparing for Engineering Schools

Table of Contents

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


No. of pages:
© ISTE Press - Elsevier 2017
23rd May 2017
ISTE Press - Elsevier
Hardcover ISBN:
eBook ISBN:

About the Author

Vincent Pavan

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.

Affiliations and Expertise

Vincent Pavan, Aix-Marseille University, France


"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

Ratings and Reviews