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<p>We give some new EP-like properties related to the (<i>b</i>,&#xa0;<i>c</i>)-inverse. It is shown that Bott–Duffin (<i>e</i>,&#xa0;<i>f</i>)-inverses have more nice implications than (<i>b</i>,&#xa0;<i>c</i>)-inverses. In particular, we study the EP-like properties of two proper subclasses of Bott–Duffin (<i>e</i>,&#xa0;<i>f</i>)-inverses, which are called orthogonal Bott–Duffin (<i>e</i>,&#xa0;<i>f</i>)-inverses and semi-central Bott–Duffin (<i>e</i>,&#xa0;<i>f</i>)-inverses. Many examples and counter-examples to illustrate the implications are included. Some results in Drazin (Linear Algebra Appl 669:136–146, 2023) are improved and extended.</p>

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Further results on EP-like properties of \(\varvec{(b,c)}\)-inverses

  • 期刊论文

  • 发表日期：

    2025年8月22日

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  • Li Fang,
  • Wenxi Li,
  • Liang Zhao

摘要

We give some new EP-like properties related to the (b, c)-inverse. It is shown that Bott–Duffin (e, f)-inverses have more nice implications than (b, c)-inverses. In particular, we study the EP-like properties of two proper subclasses of Bott–Duffin (e, f)-inverses, which are called orthogonal Bott–Duffin (e, f)-inverses and semi-central Bott–Duffin (e, f)-inverses. Many examples and counter-examples to illustrate the implications are included. Some results in Drazin (Linear Algebra Appl 669:136–146, 2023) are improved and extended.