Subdirect sums of strong \(SDD_{1}\) matrices

Some sufficient conditions ensuring that the subdirect sum of strong \(SDD_{1}\) $SD{D}_1$ matrices is in the class of strong \(SDD_{1}\) $SD{D}_1$ matrices, are presented. These sufficient conditions only depend on the elements of given matrices, and so they provide some simple criteria for applications. Moreover, numerical examples are given to illustrate the conditions presented.