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Smarandache, F., & Vasantha Kandasamy, W. B. (2013). N-Linear Algebra of Type 1 and Its Applications. Retrieved from http://gutenberg.us/

Description
This book has four chapters. The first chapter just introduces n-group which is essential for the definition of n-vector spaces and n-linear algebras of type I. Chapter two gives the notion of n-vector spaces and several related results which are analogues of the classical linear algebra theorems. In case of n-vector spaces we can define several types of linear transformations. The applications of these algebraic structures are given in Chapter 3. Chapter four gives some problem to make the subject easily understandable.

Summary
With the advent of computers one needs algebraic structures that can simultaneously work with bulk data. One such algebraic structure namely n-linear algebras of type I are introduced in this book and its applications to n-Markov chains and n-Leontief models are given. These structures can be thought of as the generalization of bilinear algebras and bivector spaces. Several interesting n-linear algebra properties are proved.

Excerpt
n-VECTOR SPACES OF TYPE I AND THEIR PROPERTIES
In this chapter we introduce the notion of n-vector spaces and describe some of their important properties. Here we define the concept of n-vector spaces over a field which will be known as the type I n-vector spaces or n-vector spaces of type I. Several interesting properties about them are derived in this chapter.
DEFINITION 2.1: A n-vector space or a n-linear space of type I (n 2)

Table of Contents
Preface 5
Chapter One
BASIC CONCEPTS 7
Chapter Two
n-VECTOR SPACES OF TYPE I AND THEIR
PROPERTIES 13
Chapter Three
APPLICATIONS OF n-LINEAR ALGEBRA OF TYPE I 81
Chapter Four
SUGGESTED PROBLEMS 103
FURTHER READING 111
INDEX 116
ABOUT THE AUTHORS 120