New results on subdirect sums of Nekrasov matrices

This paper investigates sufficient conditions for the k-subdirect sum $ B\oplus _k A $ B circle plus kA to be a Nekrasov matrix, where A is a Nekrasov matrix and B is a strictly diagonally dominant matrix. Specifically, for k = 1, the 1-subdirect sum $ A\oplus _1 B $ A circle plus 1B is shown to be a Nekrasov matrix, whereas $ B\oplus _1 A $ B circle plus 1A is not necessarily a Nekrasov matrix. To address this discrepancy, we propose two sufficient conditions under which $ B\oplus _1 A $ B circle plus 1A can be ensured to be a Nekrasov matrix. This paper not only addresses partly the question posed by Li et al. in their paper titled 'On subdirect sums of Nekrasov matrices' (Linear and Multilinear Algebra, 72(6): 1044-1055, 2024), but also enhances the theoretical understanding of the closure property of subdirect sums for Nekrasov matrices.