```	%0 Journal Article
%A Yongxin Yuan and  Hao Liu
%D 2010
%J International Journal of Mathematical and Computational Sciences
%B World Academy of Science, Engineering and Technology
%I Open Science Index 43, 2010
%T The Inverse Problem of Nonsymmetric Matrices with a Submatrix Constraint and its Approximation
%U https://publications.waset.org/pdf/3805
%V 43
%X In this paper, we first give the representation of the general solution of the following least-squares problem (LSP): Given matrices X &isin; Rn&times;p, B &isin; Rp&times;p and A0 &isin; Rr&times;r, find a matrix A &isin; Rn&times;n such that XT AX &minus; B = min, s. t. A([1, r]) = A0, where A([1, r]) is the r&times;r leading principal submatrix of the matrix A. We then consider a best approximation problem: given an n &times; n matrix A&tilde; with A&tilde;([1, r]) = A0, find A&circ; &isin; SE such that A&tilde; &minus; A&circ; = minA&isin;SE A&tilde; &minus; A, where SE is the solution set of LSP. We show that the best approximation solution A&circ; is unique and derive an explicit formula for it. Keyw

%P 861 - 865
```