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<p>Subdirect sums play an important role in a variety of practical applications, and one of the significant properties for subdirect sums is the closure property on the <i>k</i>-subdirect sum, i.e., the <i>k</i>-subdirect sum of two matrices in one class of matrices lies in the same class. In this paper, some new sufficient conditions ensuring that the <i>k</i>-subdirect sum of <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13160_2025_693_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="47" /> </InlineMediaObject> <EquationSource Format="TEX">\(SD{D_1}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>S</mi> <mi>D</mi> <msub> <mi>D</mi> <mn>1</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> matrices is also an <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13160_2025_693_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="47" /> </InlineMediaObject> <EquationSource Format="TEX">\(SD{D_1}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>S</mi> <mi>D</mi> <msub> <mi>D</mi> <mn>1</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> matrix are given. In addition, several examples are presented to illustrate the results presented.</p>

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On k-subdirect sums of \(SD{D_1}\) matrices

  • 期刊论文

  • 发表日期：

    2025年2月17日

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  • Jiaqi Qi,
  • Keru Wen,
  • Yaqiang Wang

摘要

Subdirect sums play an important role in a variety of practical applications, and one of the significant properties for subdirect sums is the closure property on the k-subdirect sum, i.e., the k-subdirect sum of two matrices in one class of matrices lies in the same class. In this paper, some new sufficient conditions ensuring that the k-subdirect sum of \(SD{D_1}\) S D D 1 matrices is also an \(SD{D_1}\) S D D 1 matrix are given. In addition, several examples are presented to illustrate the results presented.