Perturbation Theory for Core and Core-EP Inverses of Tensor via Einstein Product

Abstract

In this paper, for given tensors $\mathcal{A}$, $\mathcal{E}$ and $\mathcal{B}=\mathcal{A}+\mathcal{E}$, we investigate the perturbation bounds for the core inverse $\mathcal{A}^{\tiny\textcircled{\#}}$ and core-EP inverse $\mathcal{A}^{\oplus}$ under some conditions via Einstein product.