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**The least squares solution with the minimal norm to a system of mixed generalized Sylvester reduced biquaternion tensor equations.**
*(English)*
Zbl 1515.15028

Summary: In this paper, we investigate the least squares solution with the minimal norm to the system (1.1) over reduced biquaternion via complex representation of reduced biquaternion tensors and the Moore-Penrose inverse of tensors. Besides, we establish some necessary and sufficient conditions for the solvability to the above system and give an expression of the general solution to the system when the solvability conditions are met. Moreover, the algorithm and numerical example are presented to verify the main results of this paper.

### MSC:

15A69 | Multilinear algebra, tensor calculus |

15A09 | Theory of matrix inversion and generalized inverses |

15A24 | Matrix equations and identities |

### Keywords:

complex representation; least squares solution; reduced biquaternion tensor; Sylvester tensor equations
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\textit{A. Wei} et al., Taiwanese J. Math. 27, No. 2, 259--276 (2023; Zbl 1515.15028)

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### References:

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