Perturbation theory for Moore-Penrose inverse of tensor via Einstein product

The spectral norm of an even-order tensor is defined and investigated. An equivalence between the spectral norm of tensors and matrices is given. Using derived representations of some tensor expressions involving the Moore-Penrose inverse, we investigate the perturbation theory for the Moore-Penrose inverse of tensor via Einstein product. The classical results derived by Stewart (SIAM Rev 19:634-662, 1977) and Wedin (BIT 13:217-232, 1973) for the matrix case are extended to even-order tensors. An implementation in the Matlab programming language is developed and used in deriving appropriate numerical examples.