## N-Linear Algebra of Type I and Its Applications

**Authors:** W. B. Vasantha Kandasamy, Florentin Smarandache

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.
This book has four chapters. The first chapter just
introduces n-group which is essential for the definition of nvector
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 notion of n-best approximations can be used for error
correction in coding theory. The notion of n-eigen values can be
used in deterministic modal superposition principle for
undamped structures, which can find its applications in finite
element analysis of mechanical structures with uncertain
parameters. Further it is suggested that the concept of nmatrices
can be used in real world problems which adopts fuzzy
models like Fuzzy Cognitive Maps, Fuzzy Relational Equations
and Bidirectional Associative Memories. The applications of
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these algebraic structures are given in Chapter 3. Chapter four
gives some problem to make the subject easily understandable.
The authors deeply acknowledge the unflinching support of
Dr.K.Kandasamy, Meena and Kama.

**Comments:** 120 pages

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### Submission history

[v1] 11 Mar 2010

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