Lets={A ∈ SRn×n ｜‖ AZ-Y‖=min} where Z,Y ∈ Rn×k, SRnxn={A ∈ Rn×n] AT = A}, ‖.‖ is the Frobenius norm. We consider the following problems: Problem I. Given X, B ∈ Rn×m, find A ∈ S ∩ Pn such that AX=B, where Pn={A ∈ SRn×n ｜Ax ∈ Rn, xTAx ≥0}. oblem II. Given A ∈ Rn×n, find A ∈ SE, such that ‖A-A‖=inf ‖A-A‖, VAESE where SE is the solution set of Problem I. The sufficient and necessary condition under which SE is nonempty is obtained. The general form of SE is given. Then expression of the solution A of problem II is presented and the numerical method is described.