## Mathematics and Statistics Faculty and Staff Publications

#### Document Type

Book

#### Publication Date

2008

#### Abstract

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.

#### Publisher

InfoLearnQuest, Ann Arbor

#### ISSN

978-1-59973-031-8

#### Language (ISO)

English

#### Keywords

n-vector spaces of type II, n-linear algebra of type II

#### Recommended Citation

Smarandache, Florentin and W.B. Vasantha Kandasamy. "n-LINEAR ALGEBRA OF TYPE II." (2008). https://digitalrepository.unm.edu/math_fsp/206

#### Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

#### Included in

Algebra Commons, Algebraic Geometry Commons, Analysis Commons, Geometry and Topology Commons, Harmonic Analysis and Representation Commons