摘要
我们定义 { 我 } 反(i = 1， 2， 5 ) 并且张肌的组逆基于张肌的一个一般产品。我们在解决张肌方程和块张肌的计算公式上探索张肌的概括的逆的性质。我们使用 { 1 } 张肌的逆由张肌代表了给一个 multilinear 系统的解决方案。代表为 { 1 } 逆和一些块张肌的组逆被建立。
We define the {i}-inverse （i = 1,2, 5） and group inverse of tensors based on a general product of tensors. We explore properties of the generalized inverses of tensors on solving tensor equations and computing formulas of block tensors. We use the {1}-inverse of tensors to give the solutions of a multilinear system represented by tensors. The representations for the {1}-inverse and group inverse of some block tensors are established.
基金
The authors are very grateful to the referees for their valuable suggestions, which have considerably improved the paper. Yimin Wei was supported by the International Cooperation Project of Shanghai Municipal Science and Technology Commission （Grant No. 16510711200） and the National Natural Science Foundation of China （Grant No. 11771099）
Changjiang Bu was supported by the National Natural Science Foundation of China （Grant No. 11371109）.
关键词
张量
群逆
数学
理论研究
Tensor
generalized inverse
tensor equation
general product of tensor
