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arXiv · 2412.05799

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

Hongwei Jin·Siran Chen·Shaowu Huang·Predrag S. Stanimirović
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Abstract

We study extensions of the GD tensor inverse using the M-product. The aim of current research is threefold. In the first place, the tensor GD inverse under the M-product is introduced and considered. 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 given. In addition, 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.

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Hongwei Jin, Siran Chen, Shaowu Huang, Predrag S. Stanimirović. 2024-12-08. On the extensions of the GD inverse of tensors via the M-Product. https://arxiv.org/abs/2412.05799

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