Generalized inverses of tensors via a general product of tensors
Abstract
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.
Keywords
Tensor generalized inverse tensor equation general product of tensorMSC
15A09 15A69 65F20 65F15Preview
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Notes
Acknowledgements
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).
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