摘要
对四元数体上某类自共轭矩阵方程,在两两可交换的前提下,研究了矩阵方程的极小Frobenius范数最小二乘解.同时,在有解条件下给出了通解的表达形式.利用四元数体上自共轭矩阵奇异值分解的充分必要条件,运用四元数体上Frobenius范数正交矩阵乘积不变性,讨论了某类矩阵方程的最小二乘解,给出了极小Frobenius范数最小二乘解及其通解的表达形式,进而推广到了更为一般的矩阵方程.
For certain types self-conjugate matrix equation on quaternion field, we studied the minimal Frobenius norm least square solution of matrix equation under the premise of exchangeable, and gave the solution of general solution form under the condition of the solvability. By using sufficient and necessary conditions of the self-coniugate matrix singular value decomposition on quaternions, and invariance of Frobenius norm of orthogonal matrix product on quaternion, we discussed the least-square solutions of a kind of matrix equation, and give the expression of general solution form of the minimal Frobenius norm least squares solution, and extend to the more general matix equation in further.
出处
《中北大学学报（自然科学版）》
CAS
北大核心
2016年第3期225-228,共4页
Journal of North University of China(Natural Science Edition)
关键词
四元数体
矩阵方程
奇异值分解
最小二乘解
极小范数
quaternion field
matrix equation
singular value decomposition
the least square solution
the minimum norm
