%0 Journal Article
%T THE LEAST-SQUARES SOLUTIONS WITH THE HERMITIAN-REFLEXIVE MATRIX FOR A CLASS OF MATRIX EQUATIONS<br>一类矩阵方程的埃尔米特自反最小二乘解
%A WANG Jiangtao
%A ZHANG Zhongzhi
%A XIE Dongxiu
%A LEI Xiuren
%A <br>王江涛
%A 张忠志
%A 谢冬秀
%A 雷秀仁
%J 系统科学与数学
%D 2010
%I 
%X By means of the properties of the Hermitian-reflexive matrix and the straightened matrix, this paper considers the least-squares solutions with Hermitian-reflexive for the matrix equation $AX+BY=C.$ The necessary and sufficient condition of the solutions for the matrix equation in the sets of Hermitian-reflexive matrices and the general expression of the solution are presented. Furthermore, for any two given complex matrices, the expression of the solution for relevant optimal approximate problem is derived.
%K Hermitian-reflexive matrix
%K straightened matrix
%K matrix equation
%K least-squares solution
%K optimal approximation<br>埃尔米特自反矩阵
%K 矩阵拉直
%K 矩阵方程
%K 最小二乘解
%K 最佳逼近.
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=0CD45CC5E994895A7F41A783D4235EC2&aid=FC7FE2E260CE980F697399DEB61DBFB9&yid=140ECF96957D60B2&vid=340AC2BF8E7AB4FD&iid=5D311CA918CA9A03&sid=BE14F47B38DC36BB&eid=008520E0B52E94B3&journal_id=1000-0577&journal_name=系统科学与数学&referenced_num=0&reference_num=10