Softcover ISBN:  9780821827963 
Product Code:  MMONO/108.S 
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AMS Member Price:  $132.00 
eBook ISBN:  9781470445195 
Product Code:  MMONO/108.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Softcover ISBN:  9780821827963 
eBook: ISBN:  9781470445195 
Product Code:  MMONO/108.S.B 
List Price:  $320.00 $242.50 
MAA Member Price:  $288.00 $218.25 
AMS Member Price:  $256.00 $194.00 
Softcover ISBN:  9780821827963 
Product Code:  MMONO/108.S 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470445195 
Product Code:  MMONO/108.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Softcover ISBN:  9780821827963 
eBook ISBN:  9781470445195 
Product Code:  MMONO/108.S.B 
List Price:  $320.00 $242.50 
MAA Member Price:  $288.00 $218.25 
AMS Member Price:  $256.00 $194.00 

Book DetailsTranslations of Mathematical MonographsVolume: 108; 1992; 131 ppMSC: Primary 15; 47; Secondary 81
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.
ReadershipGraduate students as well as experts in theoretical and mathematical physics, differential and integral equations and mathematical analysis.

Table of Contents

Chapters

Chapter I. Definition of tensor products

Chapter II. Tensors and tensor algebras

Chapter III. Exterior algebra and its applications

Chapter IV. Algebraic systems with bilinear multiplication. Lie algebras


Reviews

This book provides a wellorganized 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


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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.

Chapters

Chapter I. Definition of tensor products

Chapter II. Tensors and tensor algebras

Chapter III. Exterior algebra and its applications

Chapter IV. Algebraic systems with bilinear multiplication. Lie algebras

This book provides a wellorganized 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