On Tensor Generalized Inverse And A Class Of Constrained Optimal Approximation Problem

This paper mainly studies the solution of tensor generalized inverse and a kind of con-straint matrix(second order tensor)problem,this paper is divided into Four parts.In the first part,we first introduce the research background of tensor generalized inverse and constraint matrix,the current situation at home and abroad,We also introduced some symbols and theorems to be used in this article.In the second part,we first give some properties of the inverse of core through the singu-lar value decomposition of tensor A,and then give the definitions of tensor minus order and core order.At last,the minimum norm least squares solution of the tensor equation is solved by the block form of tensor.In the third part,we give the definition and properties of the third-order tensors core inverse,core-EP inverse,and WG inverse through fast Fourier transform and Block theory circulant matrix.In the fourth part,we study a rank constrained matrix approximation in the Frobenius norm:(?)?AXA~*-B?_F~2,where k is a nonnegative integar,X is Hermitian matrix.By using the singular value decompo-sition and spectrum decomosition,we derive some conditions for the existence of Hermitian solutions,and establish general forms for the Hermitian solution to this matrix approximation problem.