摘要
在四元数体Ω上引入了自反向量、自反矩阵和广义自反矩阵等概念,利用广义自反矩阵和广义反自反矩阵的性质讨论了线性方程组AX =b、矩阵方程AX =B及AXB =C的最小二乘解问题:当A为广义自反矩阵或广义反自反矩阵时,可将线性方程组AX =b的最小二乘解问题化为两个较小独立的子问题去讨论;当A、B都是广义自反矩阵或广义反自反矩阵时,可将矩阵方程AX =B的最小二乘解问题化为线性方程组的最小二乘解问题去讨论.
Firstly, the concepts of reflexive vector, reflexive matrices, generalization reflexive matrices and etc, are introduced over quaternion field. Then by using the properties of the generalization reflexive (antireflexive) matrices the problems are discussed that least square solutions of systems of linear equation AX=b, matrices equation AX=B and AXB=C. When A is the generalization reflexive (antireflexive) matrices, least-squares problems of systems of linear equation AX=b can be decomposed into two smaller and independent subproblems to discuss; When A, B are both the generalization reflexive(antireflexive) matrices, least-squares problems of matrix equation AX=B can be decomposed into least-squares problems of systems of linear equation to discuss.
出处
《许昌学院学报》
CAS
2005年第2期7-11,共5页
Journal of Xuchang University
基金
国家自然科学基金资助项目 (60 3 64 0 0 1)
关键词
四元数体
矩阵方程
最小二乘解
quaternion field
matrix equations
least square solution
