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Author: W. B. Vasantha Kandasamy
Publisher: Infinite Study
ISBN: 1931233756
Category : Mathematics
Languages : en
Pages : 175
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Book Description
In this book the author analyzes the Smarandache linear algebra, and introduces several other concepts like the Smarandache semilinear algebra, Smarandache bilinear algebra and Smarandache anti-linear algebra. We indicate that Smarandache vector spaces of type II will be used in the study of neutrosophic logic and its applications to Markov chains and Leontief Economic models ? both of these research topics have intense industrial applications. The Smarandache linear algebra, is defined to be a Smarandache vector space of type II, on which there is an additional operation called product, such that for all a, b in V, ab is in V.The Smarandache vector space of type II is defined to be a module V defined over a Smarandache ring R such that V is a vector space over a proper subset k of R, where k is a field.
Author: W. B. Vasantha Kandasamy
Publisher: Infinite Study
ISBN: 1931233756
Category : Mathematics
Languages : en
Pages : 175
Get Book Here
Book Description
In this book the author analyzes the Smarandache linear algebra, and introduces several other concepts like the Smarandache semilinear algebra, Smarandache bilinear algebra and Smarandache anti-linear algebra. We indicate that Smarandache vector spaces of type II will be used in the study of neutrosophic logic and its applications to Markov chains and Leontief Economic models ? both of these research topics have intense industrial applications. The Smarandache linear algebra, is defined to be a Smarandache vector space of type II, on which there is an additional operation called product, such that for all a, b in V, ab is in V.The Smarandache vector space of type II is defined to be a module V defined over a Smarandache ring R such that V is a vector space over a proper subset k of R, where k is a field.
Author: W. B. Vasantha Kandasamy
Publisher: Infinite Study
ISBN: 1599730294
Category : Mathematics
Languages : en
Pages : 346
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Book Description
Set linear algebras, introduced by the authors in this book, are the most generalized form of linear algebras.These structures make use of very few algebraic operations and are easily accessible to non-mathematicians as well.The dominance of computers in everyday life calls for a paradigm shift in the concepts of linear algebra. The authors believe that set linear algebra will cater to that need.
Author: W. B. Vasantha Kandasamy
Publisher: Infinite Study
ISBN: 1599730650
Category : Mathematics
Languages : en
Pages : 295
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Book Description
Super Linear Algebras are built using super matrices. These new structures can be applied to all fields in which linear algebras are used. Super characteristic values exist only when the related super matrices are super square diagonal super matrices.Super diagonalization, analogous to diagonalization is obtained. These newly introduced structures can be applied to Computer Sciences, Markov Chains, and Fuzzy Models.
Author: W. B. Vasantha Kandasamy, Florentin Smarandache
Publisher: Infinite Study
ISBN: 1599731266
Category : Mathematics
Languages : en
Pages : 249
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Book Description
Interval Arithmetic, or Interval Mathematics, was developed in the 1950s and 1960s as an approach to rounding errors in mathematical computations. However, there was no methodical development of interval algebraic structures to this date.This book provides a systematic analysis of interval algebraic structures, viz. interval linear algebra, using intervals of the form [0, a].
Author: W. B. Vasantha Kandasamy
Publisher: Infinite Study
ISBN: 1599730855
Category : Mathematics
Languages : en
Pages : 141
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Book Description
We study these new Smarandache algebraic structures, which are defined as structures which have a proper subset which has a weak structure.A Smarandache Weak Structure on a set S means a structure on S that has a proper subset P with a weaker structure.By proper subset of a set S, we mean a subset P of S, different from the empty set, from the original set S, and from the idempotent elements if any.A Smarandache Strong Structure on a set S means a structure on S that has a proper subset P with a stronger structure.A Smarandache Strong-Weak Structure on a set S means a structure on S that has two proper subsets: P with a stronger structure, and Q with a weaker structure.
Author: Jean Dieudonné
Publisher:
ISBN:
Category : Algebras, Linear
Languages : en
Pages : 422
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Book Description
Author: Florentin Smarandache
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 21
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Book Description
In this chapter, we introduce neutrosophic triplet cosets for neutrosophic triplet G-module and neutrosophic triplet quotient G-module. Then, we give some definitions and examples for neutrosophic triplet quotient G-module and neutrosophic triplet cosets. Also, we obtain isomorphism theorems for neutrosophic triplet G-modules and we prove isomorphism theorems for neutrosophic triplet G-modules.
Author: W. B. Vasantha Kandasamy
Publisher: Infinite Study
ISBN: 1599730278
Category : Mathematics
Languages : en
Pages : 280
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Book Description
This book introduces the concept of fuzzy super matrices and operations on them. The author has provided only those operations on fuzzy supermatrices that are essential for developing super fuzzy multi expert models. We do not indulge in labourious use of suffixes or superfixes and difficult notations; instead we illustrate the working by simple examples. This book will be highly useful to social scientists who wish to work with multi expert models. An important feature of this book is its simple approach. Illustrations are given to make the method of approach to the problems easily understandable. Super fuzzy models using Fuzzy Cognitive Maps, Fuzzy Relational maps, Bidirectional Associative Memories and Fuzzy Associative Memories are defined here. Every model is a multi expert model. This book will certainly be a boon not only to social scientists but also to engineers, students, doctors and researchers. The authors introduce thirteen multi expert models using the notion of fuzzy supermatrices. These models are also described by illustrative examples.
Author: W. B. Vasantha Kandasamy
Publisher: Infinite Study
ISBN: 1931233977
Category : Mathematics
Languages : en
Pages : 238
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Book Description
In the modern age of development, it has become essential for any algebraic structure to enjoy greater acceptance and research significance only when it has extensive applications to other fields.This new algebraic concept, Linear Bialgebra, is one that will find applications to several fields like bigraphs, algebraic coding/communication theory (bicodes, best biapproximations), Markov bichains, Markov bioprocess and Leonief Economic bimodels: these are also brought out in this book.Here, the linear bialgebraic structure is given sub-bistructures and super-structures called the smarandache neutrosophic linear bialgebra which will easily yield itself to the above applications.
Author: W. B. Vasantha Kandasamy, Florentin Smarandache, K. Ilanthenral
Publisher: Infinite Study
ISBN: 1599730057
Category : Mathematics
Languages : en
Pages : 352
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Book Description
