Perturbation analysis for t-product based tensor inverse, Moore-Penrose inverse and tensor system

07/20/2021

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by   Zhengbang Cao, et al.

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This paper establishes some perturbation analysis for the tensor inverse, the tensor Moore-Penrose inverse and the tensor system based on the t-product. In the settings of structured perturbations, we generalize the Sherman-Morrison-Woodbury (SMW) formula to the t-product tensor scenarios. The SMW formula can be used to perform sensitivity analysis for a multilinear system of equations.