四元数矩阵方程AXAH=B的最小二乘解

摘要

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.%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.