Subdirect Sums Of MB-Matrices

A lot of data that collects in research and application is stored and represented by matrix,in science,engineering technology and management.Therefore,these data can be transformed into matrices to research and treat.The concept of matrix subdirect sum is proposed in several studies,such as in matrix completion problems,overlapping subdomains in domain decomposition methods and global stiffness matrices in finite elements.In these studies,it is one of the important questions to study whether the subdirect sum of a certain matrix class still is in the same class.In this paper,a special matrix with important application background——MB-matrices and the subdirect sum of MB-matrices are studied by using the matrix splitting and matrix blocking.Properties of MB-matrices and several sufficient conditions and necessary and sufficient conditions ensuring that the subdirect sum of MB-matrices is in the class of MB-matrices are given.And the conclusion is illustrated by a numerical example.