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

Description
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.

Summary
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.

Excerpt
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