数学研究
數學研究
수학연구
JOURNAL OF MATHEMATICAL STUDY
2003年
2期
145-150
,共6页
四元数矩阵方程%最小二乘解%Hermitian解%奇异值分解
四元數矩陣方程%最小二乘解%Hermitian解%奇異值分解
사원수구진방정%최소이승해%Hermitian해%기이치분해
quaternion matrix equation%hermitian solution%least-square solution%singular-value decomposition
引入了四元数矩阵范数的概念,通过使用四元数矩阵的奇异值分解,给出了四元数矩阵方程AXAH=B在最小二乘意义下的Hermitian解以及Skew-Hermitian解.
引入瞭四元數矩陣範數的概唸,通過使用四元數矩陣的奇異值分解,給齣瞭四元數矩陣方程AXAH=B在最小二乘意義下的Hermitian解以及Skew-Hermitian解.
인입료사원수구진범수적개념,통과사용사원수구진적기이치분해,급출료사원수구진방정AXAH=B재최소이승의의하적Hermitian해이급Skew-Hermitian해.
In this paper, the norms of quaternion matrices are introduced. By applying the singular value decomposition on quaternion matrices, we obtain the general expression of the least-square solutions of the matrix equation AXAH=B under the restriction that the solution matrix X∈Qn×n is Hermitian (or Skew-Hermitian), where A∈Qm×n and B∈Qm×m are given matrices.
