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<p>Let <i>A</i>, <i>W</i> be two <i>n</i> × <i>n</i> complex matrices. We present the expression of the <i>W</i>-core inverse of <i>A</i> by Hartwig and Spindelböck’s decompositions and full rank decompositions. It is also proved that <i>A</i> is <i>W</i>-core invertible if and only if <i>A</i> is right <i>W</i>-core invertible. This equivalence may not be true in a general *-ring, see H. H. Zhu, L. Y. Wu, D. Mosić (2023). Then, several results for the reverse order law of the <i>W</i>-core inverse are given. Another accomplishment of this paper is to establish some perturbation properties and perturbation bounds for the <i>W</i>-core inverse, under some conditions. Finally, the necessary and sufficient condition for the continuity of the <i>W</i>-core inverse is derived.</p>

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New results on the W-core inverse of matrices

  • 期刊论文

  • 发表日期：

    2026年5月5日

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  • Mingyue Chen,
  • Huihui Zhu,
  • Bing Dong,
  • Dijana Mosić

摘要

Let A, W be two n × n complex matrices. We present the expression of the W-core inverse of A by Hartwig and Spindelböck’s decompositions and full rank decompositions. It is also proved that A is W-core invertible if and only if A is right W-core invertible. This equivalence may not be true in a general *-ring, see H. H. Zhu, L. Y. Wu, D. Mosić (2023). Then, several results for the reverse order law of the W-core inverse are given. Another accomplishment of this paper is to establish some perturbation properties and perturbation bounds for the W-core inverse, under some conditions. Finally, the necessary and sufficient condition for the continuity of the W-core inverse is derived.