Matrices with dominating diagonal blocks

In mathematical economics we appeal frequently to the theory of matrices with dominating diagonal elements. This paper generalizes that theory to the case of matrices with dominating diagonal submatrices which appear to possess the same fundamental properties. Matrix dominance is defined, and its connection with “bigness” of a matrix is established. Quick checks for dominance are developed. The standard theorems associated with dominating diagonal matrices are shown to be special cases of more general results. Examples are presented to illustrate the wide range of possible application.