N-Linear Algebra of Type II

Authors: W. B. Vasantha Kandasamy, Florentin Smarandache

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 case of n-linear algebra of type II, we are in a position to define linear functionals which is one of the marked difference between the n-vector spaces of type I and II. However all the applications mentioned in n-linear algebras of type I can be appropriately extended to n-linear algebras of type II. Another use of n-linear algebra (n-vector spaces) of type II is that when this structure is used in coding theory we can have different types of codes built over different finite fields whereas this is not possible in the case of n-vector spaces of type I. Finally in the case of n-vector spaces of type II we can obtain neigen values from distinct fields; hence, the n-characteristic polynomials formed in them are in distinct different fields. An attractive feature of this book is that the authors have suggested 120 problems for the reader to pursue in order to understand this new notion. 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 6 suggests over a hundred problems. It is important that the reader should be well versed with not only linear algebra but also nlinear algebras of type I.

Comments: 231 pages

Download: PDF

Submission history

[v1] 11 Mar 2010

Unique-IP document downloads: 174 times is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus