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

Jing Xia; Jing Xia

doi:10.3934/math.2022039

AIMS Mathematics

2022, Volume 7, Issue 1: 617-631. doi: 10.3934/math.2022039

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

Jing Xia ^,

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

Received: 28 July 2021 Accepted: 23 September 2021 Published: 14 October 2021
MSC : 15A06, 15A42, 15A60

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\bigoplus_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.
- subdirect sum,
- $ \{i_0\} $-Nekrasov matrices,
- $ S $-Nekrasov matrices
Citation: Jing Xia. Note on subdirect sums of $ \{i_0\} $-Nekrasov matrices[J]. AIMS Mathematics, 2022, 7(1): 617-631. doi: 10.3934/math.2022039

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Abstract

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\bigoplus_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.

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