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<p>A square complex matrix <i>A</i> is referred to as core-EP if <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( A^{\dagger }A_{c}=A_{c}A^{\dagger }\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>A</mi> <mo>†</mo> </msup> <msub> <mi>A</mi> <mi>c</mi> </msub> <mo>=</mo> <msub> <mi>A</mi> <mi>c</mi> </msub> <msup> <mi>A</mi> <mo>†</mo> </msup> </mrow> </math></EquationSource> </InlineEquation>, where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(A_{c}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>A</mi> <mi>c</mi> </msub> </math></EquationSource> </InlineEquation> denotes the core-part of <i>A</i>, and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(A^\dagger \)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>A</mi> <mo>†</mo> </msup> </math></EquationSource> </InlineEquation> represents the Moore-Penrose inverse of <i>A</i>. In this paper, some equivalent conditions of core-EP matrices are investigated. Also, characterizations of <i>DMP-</i>inverses, <i>MPD-</i>inverses, and <i>CMP-</i>inverses are given. Finally, applications in solving singular linear systems arising from a discretization of a PDE are studied.</p>

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Characterizations of core-EP matrices with applications to singular equations

  • 期刊论文

  • 发表日期：

    2026年2月3日

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  • Ehsan Kheirandish,
  • Abbas Salemi,
  • Néstor Thome

摘要

A square complex matrix A is referred to as core-EP if \( A^{\dagger }A_{c}=A_{c}A^{\dagger }\) A † A c = A c A † , where \(A_{c}\) A c denotes the core-part of A, and \(A^\dagger \) A † represents the Moore-Penrose inverse of A. In this paper, some equivalent conditions of core-EP matrices are investigated. Also, characterizations of DMP-inverses, MPD-inverses, and CMP-inverses are given. Finally, applications in solving singular linear systems arising from a discretization of a PDE are studied.