矩阵方程AXB=C的最小二乘解的定秩研究  

On the Rank Range of the Least-squares Solutions of the Matrix Equation AXB=C

作　　者：孟纯军[1] 李桃珍 

机构地区：[1]湖南大学数学与计量经济学院,湖南长沙410082

出　　处：《湖南大学学报（自然科学版）》2013年第7期92-94,共3页Journal of Hunan University:Natural Sciences

基　　金：国家自然科学基金资助项目(11271117)

摘　　要：研究了矩阵方程AXB=C最小二乘解的秩的范围,利用矩阵的奇异值分解以及Frobenius范数的特征,得到了秩约束下最小二乘解的表达式,并得到了最大秩和最小秩最小二乘解.This paper, we considered the rank range of the least-squares solutions of matrix equation AXB = C. By applying the singular value decomposition of matrix and the properties of Frobenius matrix norm, we have obtained the range of the rank and the least-squares solution expression of under rank con- strained. Finally, we have provided the expressions of the least-squares solutions with maximal and mini- mum rank respectively.

关 键 词：最优控制 最小二乘解 秩约束 奇异值分解 FROBENIUS范数 

分 类 号：O241.6[理学—计算数学]