Open AccessBook
Interval Linear Algebra
W. B. Vasantha Kandasamy,Florentin Smarandache +1 more
- 16 Nov 2010
TL;DR: In this article, the authors use only special types of intervals and introduce the notion of different types of interval linear algebras and interval vector spaces using the intervals of the form [0, a] where the intervals are from Zn or Z+ \cup {0} or Q+ √ {0] or R+ ǫ or Rǫ √ǫ.
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Abstract: In this book we use only special types of intervals and introduce the notion of different types of interval linear algebras and interval vector spaces using the intervals of the form [0, a] where the intervals are from Zn or Z+ \cup {0} or Q+ \cup {0} or R+ \cup {0} A systematic development is made starting from set interval vector spaces to group interval vector spaces Vector spaces are taken as interval polynomials or interval matrices or just intervals over suitable sets or semigroups or groups Main feature of this book is the authors have given over 350 examples This book has six chapters Chapter one is introductory in nature Chapter two introduces the notion of set interval linear algebras of type one and two Set fuzzy interval linear algebras and their algebras and their properties are discussed in chapter three Chapter four introduces several types of interval linear bialgebras and bivector spaces and studies them The possible applications are given in chapter five Chapter six suggests nearly 110 problems of all levels
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Citations
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Innovative Uses of Matrices
Florentin Smarandache,W. B. Vasantha Kandasamy,Indra Venkatbabu +2 more
- 02 Mar 2013
TL;DR: This book describes the innovative ways in which matrices have been used, starting from ATD, RTD & CETD matrices which can be applied to any collected data depending on time, to fuzzy linguistic matrices, which play a major role in the construction of fuzzy linguistic models.
References
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Fuzzy sets
Lotfi A. Zadeh
- 01 Aug 1996
TL;DR: A separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
53.2K
Finite Markov Chains.
TL;DR: This lecture reviews the theory of Markov chains and introduces some of the high quality routines for working with Markov Chains available in QuantEcon.jl.
1.7K
•Book
Topics in algebra
I. N. Herstein
- 01 Jan 1964
TL;DR: In this paper, the authors propose preliminary notions of group theory and group theory for group spaces and modules, including linear transformations and vector spaces. But they do not discuss group theory.
1K
On the Structure of Abstract Algebras
Garrett Birkhoff,P. Hall +1 more
- 01 Oct 1935
TL;DR: In this paper, a study of abstract algebra qua abstract algebras is presented, where no vocabulary suitable for this purpose is current, and they have been forced to use a number of new terms, and extend the meaning of some accepted ones.
1K
•Book
Advanced linear algebra
Steven Roman
- 01 Jan 1992
TL;DR: Jafarian as discussed by the authors provides an encyclopedic treatment of linear algebra theory, both classical and modern, with an extensive bibliography, including a new chapter on associative algebras that includes the well-known characterizations of the finite-dimensional division algebra over real fields and over finite fields.
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