ELA, Volume 16, pp. 171-182, July 2007, abstract.

Subdirect sums of doubly diagonally dominant matrices

Yan Zhu and Ting-Zhu Huang

The problem of when the k-subdirect sum of a doubly diagonally
dominant matrix (DDD matrix) is also a DDD matrix is studied. Some
sufficient conditions are given. The same situation is analyzed
for diagonally dominant matrices and strictly diagonally dominant
matrices. Additionally, some conditions are also derived when
card(S)>card(S_1) which was not studied by Bru, Pedroche
and Szyld [Electron. J. Linear Algebra, 15:201-209, 2006].
Examples are given to illustrate the conditions presented.