Subdirect Sums of $ GSD{D_1} $ matrices

Jiaqi Qi; Yaqiang Wang; Jiaqi Qi; Yaqiang Wang

doi:10.3934/era.2024179

Electronic Research Archive

2024, Volume 32, Issue 6: 3989-4010. doi: 10.3934/era.2024179

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Theory article

Subdirect Sums of $ GSD{D_1} $ matrices

Jiaqi Qi ,
Yaqiang Wang ^,

School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji 721013, China

Received: 29 January 2024 Revised: 20 May 2024 Accepted: 31 May 2024 Published: 19 June 2024

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.
- subdirect sum,
- $ H $-matrices,
- $ GSD{D_1} $ matrices,
- strictly diagonally dominant matrices,
- sufficient conditions
Citation: Jiaqi Qi, Yaqiang Wang. Subdirect Sums of $ GSD{D_1} $ matrices[J]. Electronic Research Archive, 2024, 32(6): 3989-4010. doi: 10.3934/era.2024179

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Abstract

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.

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