INTRODUCTION TO BIMATRICES

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