## 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

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### Submission history

[v1] 11 Mar 2010

**Unique-IP document downloads:** 150 times

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