摘要
一类复合线性系统的数学模型归结为求解线性矩阵方程组[A1XB1,A2XB2]=[C,D],但该方程组在一般情况下未必相容,因此研究其最小二乘解与研究其相容条件下的准确解同样具有重要意义.利用矩阵对的广义奇异值分解及Frobenius范数正交矩阵乘积不变性,给出了实矩阵方程组[A1XB1,A2XB2]=[C,D]的最小二乘解的求法及其解的表达式.
Solving the mathematical model of a class of composite linear systems is reduced to matrix equations of the form A1XB1,A2XB2]=. Since the equations of this kind are usually unsolvable, the studying its leastsquares solutions is of equal importance. In this paper, using generalized singular value decomposition of matrices and invariant of Frobenius norm of orthogonal matrix product, the expressions of the leastsquares solution on the real matrix equations 糤THX〗A= are given.
出处
《四川师范大学学报（自然科学版）》
CAS
CSCD
2003年第4期370-372,共3页
Journal of Sichuan Normal University（Natural Science）
基金
广西民族学院科研基金(02SJX0008)资助项目
