Subdirect sums of S-strictly diagonally dominant matrices

Abstract

Conditions are given which guarantee that the k-subdirect sum of S-strictly diagonally dominant matrices (S-SDD) is also S-SDD. The same situation is analyzed for SDD matrices.
The converse is also studied: given an SDD matrix C with the structure of a k-subdirect sum and
positive diagonal entries, it is shown that there are two SDD matrices whose subdirect sum is C.