The Moore-Penrose Inverse Of Quaternion Tensor Via The QT-Product

In this paper,we mainly study the characteristics and perturbation of the Moore-Penrose inverse of quaternion tensors via the QT-product.Firstly,the definitions of the norm,the null space and the range of quaternion tensors via the QT-product are proposed.Then we prove that two quaternion tensors can be multiplied by blocks via the QT-product and give the distributive law and associative law via the QT-product.Secondly,the definition of the Moore-Penrose inverse of quaternion tensors via the QT-product is given,and the existence and uniqueness of the Moore-Penrose inverse of quaternion tensors via the QT-product is proved.The expression of the Moore-Penrose inverse of quaternion tensors via the QT-product is given by the singular value decomposition via the QT-product,and illustrated by a concrete example.Perturbation analysis is carried out for the Moore-Penrose inverse of quaternion tensors via the QT-product under the conditions of one-sided,rank-preserving and two-sided,and examples are given to illustrate the perturbation results.