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<p>The P-core-EP inverse was defined as a linear combination of the core-EP inverse and projectors determined by it. Our main aim is to present new characterizations of the P-core-EP inverse as a solution of certain new systems of matrix equations. Different representations for the P-core-EP inverse are developed in terms of the Moore–Penrose inverse, projectors, and full-rank decompositions. We study the P-core-EP inverse of the upper block triangular matrix. Applying the P-core-EP inverse, we solve several linear equations and give the forms of their general solutions. Numerical examples are given in order to confirm our results.</p>

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Different characterizations of the P-core-EP inverse

  • 期刊论文

  • 发表日期：

    2025年11月8日

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  • Dijana Mosić,
  • David E. Ferreyra

摘要

The P-core-EP inverse was defined as a linear combination of the core-EP inverse and projectors determined by it. Our main aim is to present new characterizations of the P-core-EP inverse as a solution of certain new systems of matrix equations. Different representations for the P-core-EP inverse are developed in terms of the Moore–Penrose inverse, projectors, and full-rank decompositions. We study the P-core-EP inverse of the upper block triangular matrix. Applying the P-core-EP inverse, we solve several linear equations and give the forms of their general solutions. Numerical examples are given in order to confirm our results.