On the Convergence of Monotone Lattice Matrices

Jing Jiang,Lan Shu,Xin’An Tian

doi:10.4236/am.2013.46125

Abstract

Since lattice matrices are useful tools in various domains like automata theory, design of switching circuits, logic of binary relations, medical diagnosis, markov chains, computer network, traffic control and so on, the study of the properties of lattice matrices is valuable. A lattice matrix A is called monotone if A is transitive or A is monotone increasing. In this paper, the convergence of monotone matrices is studied. The results obtained here develop the corresponding ones on lattice matrices shown in the references.

Highlights

In the field of applications, lattice matrices play major role in various areas such as automata theory, design of switching circuits, logic of binary relations, medical diagnosis, markov chains, computer network, traffic control
Since several classical lattice matrices, for example transitive matrix, monotone increasing matrix, nilpotent matrix, have special applications, many authors have studied these types of matrices
A transitive matrix can be used in clustering, information retrieval, preference, and so on; a nilpotent matrix represents an acyclic graph that is used to represent consistent systems and is important in the representation of precedence relations

Summary

Introduction

In the field of applications, lattice matrices play major role in various areas such as automata theory, design of switching circuits, logic of binary relations, medical diagnosis, markov chains, computer network, traffic control (see e.g. [1]). In the field of applications, lattice matrices play major role in various areas such as automata theory, design of switching circuits, logic of binary relations, medical diagnosis, markov chains, computer network, traffic control Since several classical lattice matrices, for example transitive matrix, monotone increasing matrix, nilpotent matrix, have special applications, many authors have studied these types of matrices. A transitive matrix can be used in clustering, information retrieval, preference, and so on The transitive closure of lattice matrix has been used to analyze the maximum road of network. We continue to study transitive lattice matrices and monotone increasing matrices. The main results obtained in this paper develop the previous results on transitive lattice matrices [5] and monotone increasing matrices [6]

Definitions and Preliminaries

Convergence of Monotone Lattice Matrices