摘要
以HQn×n表示四元数Hermite矩阵的全体.给出了四元数矩阵方程AX=B在HQn×n中的最小二乘解的表达式,以及AX=B在HQn×n中有解的充分必要条件与通解的表达式.
Let Q^(m×n) be the set of m×n quaternion matrices, HQ^(n×n) be the set of n×n quaternion Hermite matrices. This paper discusses the following problems.Problem A. Given A,B∈Q^(m×n), find ∈HQ^(n×n)such that‖A-B‖_F=minX∈HQ^(n×n)‖AX-B‖_F. Problem B. Given A, B∈Q^(m×n), find X∈HQ^(n×n)such thatAX=B.The expression of the solution to problem A is provided. The necessary and sufficient conditions of problem B are presented. The general solutions of problem B are given.
出处
《洛阳大学学报》
2004年第2期1-4,共4页
Journal of Luoyang University
基金
国家自然科学基金资助项目(项目编号:10371044)
