【摘要】：In this paper, we first consider the least-squares solution of the matrix inverse problem as follows: Find a hermitian anti-reflexive matrix corresponding to a given generalized reflection matrix J such that for given matrices X, B we have min_A ‖AX-B‖. The existence theorems are obtained, and a general representation of such a matrix is presented. We denote the set of such matrices by S_E. Then the matrix nearness problem for the matrix inverse problem is discussed. That is: Given an arbitrary A~*, find a matrix A ∈S_E which is nearest to A~* in Frobenius norm. We show that the nearest matrix is unique and provide an expression for this nearest matrix.