一个四元数矩阵方程AXA~H+BYB~H=C最小二乘解问题研究

Research on the Least Square Solution to the Quaternion Matrix Equation AXA~H+BYB~H=C

摘要: 根据四元数矩阵方程的实表示方法,将四元数矩阵方程等价地表示为实数矩阵方程,再利用实数域上的矩阵方程约束解,给出了四元数矩阵方程AXAH+BYBH=C的自共轭最小二乘问题通解的表达式和自共轭最小范数最小二乘解的表达式.

Abstract: Accroding to the real representation to the quaternion matrix equation,the real representation equation is given equivalently.Further more,by using the constrained solution of matrix equation,the general self-conjugate least square solution of the quaternion matrix equation AXAH+BYBH=C and the least solution of the least norm are presented.