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 n-eigen 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 suggests over a hundred
problems. It is important that the reader is well-versed not only with linear
algebra but also n-linear algebra of type I.Comment: 229 page