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Generalized inverses of tensors via a general product of tensors |
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| Authors: | Lizhu Sun Baodong Zheng Yimin Wei Changjiang Bu |
| Affiliation: | 1. College of Science, Harbin Engineering University, Harbin 150001, China2. School of Science, Harbin Institute of Technology, Harbin 150001, China3. School of Mathematical Sciences, Shanghai Key Laboratory of Contemporary Applied Mathematics, Fudan University, Shanghai 200433, China |
| 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 tensor |
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