Outer and (b,c) inverses of tensors

Reverse-order law for core inverse of tensors

“…Further, the authors of [29], proved the following result for the range space. Using Lemma 2.9, we can easily show the following result.…”

Core and core-EP inverses of tensors

“…The orthogonal projection onto a subspace R(A) is denoted by P R(A) and defined as P R(A) = A * N A † . One specific and useful algorithm for a proper matricization of an arbitrary tensor was proposed in [28].…”

Perturbation theory for core and core-EP inverses of tensor via Einstein product

“…Definition 1.13. [15,22] Let I 1 , ..., I M , K 1 , ..., K N be given integers and I, R are the integers defined as…”

“…Also, an appropriate definition of the tensor rank, arising from the reshaping operation, was proposed in [22]. Definition 1.14.…”