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<p>Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(T:M_n\rightarrow M_n\)</EquationSource> </InlineEquation> preserve Hadamard majorization. We show that this property is satisfied by the Drazin inverse (and so the group inverse), but not by the Moore-Penrose inverse. We also give a necessary and sufficient condition for the Moore-Penrose inverse to possess this property.</p>

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Generalized inverses of linear preservers of Hadamard majorization

  • 期刊论文

  • 发表日期：

    2025年11月25日

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  • P. R. Raickwade,
  • C. C. Hsu,
  • K. C. Sivakumar

摘要

Let \(T:M_n\rightarrow M_n\) preserve Hadamard majorization. We show that this property is satisfied by the Drazin inverse (and so the group inverse), but not by the Moore-Penrose inverse. We also give a necessary and sufficient condition for the Moore-Penrose inverse to possess this property.