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<p>The main objective of this study is to introduce unique representations and characterizations for the several classes of weighted generalized inverses of matrices. Proposed representations of the matrix-weighted core inverse will help us to discuss some results associated with the reverse order law for these inverses. Furthermore, this paper introduces an extension of the concepts of generalized bilateral inverse and their respective dual for complex rectangular matrices. Characteristics that lead to self-duality in weighted bilateral inverses are also examined. In addition, a W-weighted index-MP, W-weighted MP-index, and W-weighted MP-index-MP matrices for rectangular complex matrices are introduced.</p>

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Characterizations of weighted generalized inverses

  • 期刊论文

  • 发表日期：

    2025年1月20日

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  • Bibekananda Sitha,
  • Ratikanta Behera,
  • Jajati Keshari Sahoo,
  • R. N. Mohapatra,
  • Predrag Stanimirović,
  • Alena Stupina

摘要

The main objective of this study is to introduce unique representations and characterizations for the several classes of weighted generalized inverses of matrices. Proposed representations of the matrix-weighted core inverse will help us to discuss some results associated with the reverse order law for these inverses. Furthermore, this paper introduces an extension of the concepts of generalized bilateral inverse and their respective dual for complex rectangular matrices. Characteristics that lead to self-duality in weighted bilateral inverses are also examined. In addition, a W-weighted index-MP, W-weighted MP-index, and W-weighted MP-index-MP matrices for rectangular complex matrices are introduced.