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N-Linear Algebra of Type 2

By Smarandache, Florentin

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Book Id: WPLBN0002828454
Format Type: PDF eBook:
File Size: 3.50 MB
Reproduction Date: 7/31/2013

Title: N-Linear Algebra of Type 2  
Author: Smarandache, Florentin
Language: English
Subject: Non Fiction, Education, Algebra
Collections: Mathematics, Algebra, Math, Authors Community, Literature, Most Popular Books in China, Favorites in India, Education
Publication Date:
Publisher: World Public Library
Member Page: Florentin Smarandache


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Smarandache, B. F., & Vasantha Kandasamy, W. B. (2013). N-Linear Algebra of Type 2. Retrieved from

This book has three chapters. In the first chapter the notion of n-vector spaces of type II are introduced. This chapter gives over 50 theorems. Chapter two introduces the notion of n-inner product vector spaces of type II, n-bilinear forms and n-linear functionals. The final chapter suggests over a hundred problems. It is important that the reader should be well versed with not only linear algebra but also n-linear algebras of type I.

This book is a continuation of the book n-linear algebra of type I and its applications. Most of the properties that could not be derived or defined for n-linear algebra of type I is made possible in this new structure: n-linear algebra of type II which is introduced in this book.

In this chapter we for the first time introduce the notion of n-vector space of type II. These n-vector spaces of type II are different from the n-vector spaces of type I because the n-vector spaces of type I are defined over a field F where as the n-vector spaces of type II are defined over n-fields. Some properties enjoyed by n-vector spaces of type II cannot be enjoyed by n-vector spaces of type I. To this; we for the sake of completeness just recall the definition of n-fields in section one and n-vector spaces of type II are defined in section two and some important properties are enumerated.

Table of Contents
Preface 5 Chapter One n-VECTOR SPACES OF TYPE II AND THEIR PROPERTIES 7 1.1 n-fields 7 1.2 n-vector Spaces of Type II 10 Chapter Two n-INNER PRODUCT SPACES OF TYPE II 161 Chapter Three SUGGESTED PROBLEMS 195 FURTHER READING 221 INDEX 225 ABOUT THE AUTHORS 229


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