Note on subdirect sums of $\{i_0\}$-Nekrasov matrices

The concept of $k$-subdirect sums of matrices, as a generalization of the usual sum and the direct sum, plays an important role in scientific computing. In this paper, we introduce a new subclass of $S$-Nekrasov matrices, called $\{i_0\}$-Nekrasov matrices, and some sufficient conditions are given which guarantee that the $k$-subdirect sum $A\underset{k}{⨁}B$ is an $\{i_0\}$-Nekrasov matrix, where $A$ is an $\{i_0\}$-Nekrasov matrix and $B$ is a Nekrasov matrix. Numerical examples are reported to illustrate the conditions presented.