Subdirect Sums of $GSD{D}_1$ matrices

The class of generalized $SD{D}_1\left(GSD{D}_1\right)$ matrices is a new subclass of $H$-matrices. In this paper, we focus on the subdirect sum of $GSD{D}_1$ matrices, and some sufficient conditions to ensure that the subdirect sum of $GSD{D}_1$ matrices with strictly diagonally dominant $\left(SDD\right)$ matrices is in the class of $GSD{D}_1$ matrices are given. Moreover, corresponding examples are given to illustrate our results.