四元数矩阵方程的最小二乘解

利用四元数矩阵的广义奇异值分解,给出了下列四元数矩阵方程问题‖AXB-M‖2F ‖CXD-N‖2F=min解的一般表达式.

The Least-Square Solutions to the Quaternion Matrix Equation Systems

In this paper, the following problem is considered:Given A ∈ Qm×n, B ∈ Qp×q, M ∈ Qm×q, C ∈ Ql×n, D ∈ Qp×l, N ∈ Ql×5, find X ∈ Qn×P such that‖ AXB - M ‖ 2F. + ‖ CXD - N ‖ 2F = minBy applying the generalized singular value decomposition of quaternion matrices, the general solutions of above problem are obtained.