标题： 张量的GD逆的扩展通过M-乘积 显示英文标题

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

摘要： 我们研究使用M-乘积的GD张量逆的扩展。 当前研究的目标有三个。 首先，引入并考虑在M-乘积下的张量GD逆。 我们给出了利用核心幂零分解的GD逆的几个性质和表示，然后建立了GD逆的逆序律规则。 其次，研究了张量GDMP逆，并给出了相应的数值算法。 此外，建立了GDMP逆的逆序律和顺序律。 第三，在M-乘积下的GD-Star张量逆被引入并进行了研究。 最后，研究了多线性方程的GD逆、GDMP逆和GD-Star逆解。 进行了示例数值计算。 显示英文摘要

摘要： 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.