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<p>We study extensions of the GD tensor inverse that is based on the M-product. The comprehensive aim of the current research is threefold. First, the tensor GD inverse under the M-product is introduced and considered. In that aim, we give the several properties and representations of the GD inverse using the core nilpotent decomposition and then establish the reverse-order law rules for the GD inverse. Second, the tensor GDMP inverse is studied and the corresponding numerical algorithm is specified. In addition, within this objective, the reverse- and forward-order laws of the GDMP inverse are established. Third, the GD-Star tensor inverse under the M-product is introduced and studied. Finally, the GD inverse, GDMP inverse and GD-Star inverse solutions of multilinear equations are investigated. Illustrative numerical calculation is performed.</p>

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On extensions of the GD inverse of tensors via the M-product

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • Hongwei Jin,
  • Siran Chen,
  • Shaowu Huang,
  • Predrag S. Stanimirović

摘要

We study extensions of the GD tensor inverse that is based on the M-product. The comprehensive aim of the current research is threefold. First, the tensor GD inverse under the M-product is introduced and considered. In that aim, we give the several properties and representations of the GD inverse using the core nilpotent decomposition and then establish the reverse-order law rules for the GD inverse. Second, the tensor GDMP inverse is studied and the corresponding numerical algorithm is specified. In addition, within this objective, the reverse- and forward-order laws of the GDMP inverse are established. Third, the GD-Star tensor inverse under the M-product is introduced and studied. Finally, the GD inverse, GDMP inverse and GD-Star inverse solutions of multilinear equations are investigated. Illustrative numerical calculation is performed.