## Mathematics and Statistics Faculty and Staff Publications

#### Document Type

Book

#### Publication Date

2005

#### Abstract

Matrix theory has been one of the most utilised concepts in fuzzy models and neutrosophic models. From solving equations to characterising linear transformations or linear operators, matrices are used. Matrices find their applications in several real models. In fact it is not an exaggeration if one says that matrix theory and linear algebra (i.e. vector spaces) form an inseparable component of each other. The study of bialgebraic structures led to the invention of new notions like birings, Smarandache birings, bivector spaces, linear bialgebra, bigroupoids, bisemigroups, etc. But most of these are abstract algebraic concepts except, the bisemigroup being used in the construction of biautomatons. So we felt it is important to construct nonabstract bistructures which can give itself for more and more lucid applications. So, as a first venture we have defined the notion of bimatrices. These bimatrices in general cannot be given an algebraic operation like bimatrix addition and bimatrix multiplication, so that the collection of bimatrices become closed with respect to these operations. In fact this property will be nice in a way, for, in all our analysis we would not in general get a solution from a set we have started with. Only this incompleteness led to the invention of complex number or the imaginary number “i”

#### Publisher

Hexis, Phoenix

#### ISSN

1931233-95-0

#### Language (ISO)

English

#### Keywords

bimatrice, neutrosophic bimatrice

#### Recommended Citation

Smarandache, Florentin; W.B. Vasantha Kandasamy; and K. Ilanthenral. "INTRODUCTION TO BIMATRICES." (2005). https://digitalrepository.unm.edu/math_fsp/238

#### Creative Commons License

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

#### Included in

Algebra Commons, Algebraic Geometry Commons, Analysis Commons, Discrete Mathematics and Combinatorics Commons, Other Mathematics Commons, Other Physical Sciences and Mathematics Commons