Frontiers of Mathematics in China >
Generalized inverses of tensors via a general product of tensors
Received date: 05 Jan 2018
Accepted date: 21 Mar 2018
Published date: 14 Aug 2018
Copyright
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.
Key words： Tensor; generalized inverse; tensor equation; general product of tensor
Lizhu SUN , Baodong ZHENG , Yimin WEI , Changjiang BU . Generalized inverses of tensors via a general product of tensors[J]. Frontiers of Mathematics in China, 2018 , 13(4) : 893 -911 . DOI: 10.1007/s11464-018-0695-y
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