<p>This study obtains several representations and properties of the generalized core-EP inverse (GCEP inverse). A novel canonical representation of the generalized core-EP inverse is obtained using the singular value decomposition (SVD). To accomplish this, a canonical representation of the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13226_2025_813_Article_IEq1.gif" Format="GIF" Height="27" Rendition="HTML" Resolution="72" Type="Linedraw" Width="35" /> </InlineMediaObject> <EquationSource Format="TEX">$A^{(2)}_{T,S}$</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>A</mi> <mrow> <mi>T</mi> <mo>,</mo> <mi>S</mi> </mrow> <mrow> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </math></EquationSource> </InlineEquation> is also obtained. Further, utilizing the full-rank decomposition of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13226_2025_813_Article_IEq1.gif" Format="GIF" Height="27" Rendition="HTML" Resolution="72" Type="Linedraw" Width="35" /> </InlineMediaObject> <EquationSource Format="TEX">$A^{(2)}_{T,S}$</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>A</mi> <mrow> <mi>T</mi> <mo>,</mo> <mi>S</mi> </mrow> <mrow> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </math></EquationSource> </InlineEquation>, some full-rank representations of the GCEP inverse are obtained, which in turn gives some new integral representations of the GCEP inverse. Additionally, algorithms and numerical examples are given using the representations obtained. Algorithms are implemented in Matlab R2024a, and it concluded that our algorithms are reliable and give more accurate results than the existing one in [<CitationRef CitationID="CR1">1</CitationRef>].</p>

Generalized Core-EP Inverse: Representational and Computational Aspects

期刊论文
发表日期：

2025年7月19日

查看全文

Geeta Chowdhry,
Falguni Roy

摘要

This study obtains several representations and properties of the generalized core-EP inverse (GCEP inverse). A novel canonical representation of the generalized core-EP inverse is obtained using the singular value decomposition (SVD). To accomplish this, a canonical representation of the $A^{(2)}_{T,S}$ $A_{T, S}^{(2)}$ is also obtained. Further, utilizing the full-rank decomposition of $A^{(2)}_{T,S}$ $A_{T, S}^{(2)}$ , some full-rank representations of the GCEP inverse are obtained, which in turn gives some new integral representations of the GCEP inverse. Additionally, algorithms and numerical examples are given using the representations obtained. Algorithms are implemented in Matlab R2024a, and it concluded that our algorithms are reliable and give more accurate results than the existing one in [1].