Let S={A∈Pn|AZ=Y,Z TY∈P K,R(Y T)=R(Y TZ)} where Z.Y∈R n×k ,P n={A∈R n×n |A=A T,x TAx≥0,x∈R n},R(Y T) is the column space of Y T. We consider the following Problems: Problem Ⅰ: Given X.B∈R n×m , find A∈S such that AX=B Problem Ⅱ: Given ∈R n×n , find ∈S E such that ‖-‖= inf A∈S E‖-A‖where ‖·‖ is Frobenius norm, and S E denotes the solution set of problem Ⅰ. The sufficient and necessary condition, under which S E is nonempty, is obtained. The general form of S E is given, then expression of the solution of problem Ⅱ is presented and the numerical method is described.
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