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Tensor Spaces and Exterior Algebra
Takeo Yokonuma, Sophia University, Tokyo, Japan

Translations of Mathematical Monographs
1992; 131 pp; softcover
Volume: 108
ISBN-10: 0-8218-2796-0
ISBN-13: 978-0-8218-2796-3
List Price: US$55
Member Price: US$44
Order Code: MMONO/108.S
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This book explains, as clearly as possible, tensors and such related topics as tensor products of vector spaces, tensor algebras, and exterior algebras. You will appreciate Yokonuma's lucid and methodical treatment of the subject. This book is useful in undergraduate and graduate courses in multilinear algebra.

Tensor Spaces and Exterior Algebra begins with basic notions associated with tensors. To facilitate understanding of the definitions, Yokonuma often presents two or more different ways of describing one object. Next, the properties and applications of tensors are developed, including the classical definition of tensors and the description of relative tensors. Also discussed are the algebraic foundations of tensor calculus and applications of exterior algebra to determinants and to geometry. This book closes with an examination of algebraic systems with bilinear multiplication. In particular, Yokonuma discusses the theory of replicas of Chevalley and several properties of Lie algebras deduced from them.


Graduate students as well as experts in theoretical and mathematical physics, differential and integral equations and mathematical analysis.


"This book provides a well-organized introduction to tensors and related topics and could be useful for students of different levels (including Ph.D. level). The author includes a number of exercises at the end of each chapter."

-- Mathematical Reviews

Table of Contents

  • Definition of tensor products
  • Tensors and tensor algebras
  • Exterior algebra and its applications
  • Algebraic systems with bilinear multiplication. Lie algebras
  • Exercises
  • References for the English edition
  • Subject index
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