Constructing and Representation of Lattice-Group-Class Matrix

Lattice matrices are one of the most applicable tools in various parts such as like automata theory, design of switching circuits, the logic of binary relations, medical diagnosis, Markov chains, computer networks, and traffic control. The study of lattice matrices is practical and useful for different domains. However, the relationship between a lattice-group structure and with matrix has not been studied. We continue studying matrices and lattices, finally, a new class of Matrix is constructed using a hybrid lattice group. The lattice-group-class matrix is an interesting topic to investigate and it brings new insights to the theory of Lattice and Group as well as the matrix. Moreover, the lattice-group-class matrix can be widely used in the computational analysis of the matrix. In this paper construction of lattice-group-class matrix under the influence of lattice-group and function are given. The operations under the lattice-group-class matrix are presented. In the analysis section couple of theorems are presented to analyze the lattice-group-class matrix. The algebraic structure of the lattice-group-class matrix is formulated and some of the numerical examples are presented to illustrate the proposed structure. Keywords - Lattice-Group, Lattice, Matrix, Lattice-Group-Class Matrix, Function