【摘要】 本文研究了Sylvester四元数矩阵方程A₁X₁B₁+A₂X₂B₂=C的最小二乘Hankel解的问题。将四元数矩阵的实向量表示方法和矩阵的半张量积方法联合起来，将所研究的四元数问题转化为实矩阵方程。根据Hankel矩阵的结构特征，提取了矩阵中的有效元素，构造了新的解向量，降低了所研究问题的复杂度。得到了方程存在Hankel解的条件，并给出Hankel解的一般形式。最后，给出了求解所讨论问题的算法。更多还原

【Abstract】 Least square Hankel solutions of the Sylvester quaternion matrix equation A₁X₁B₁+A₂X₂B₂=C are studied. By means of real vector representation of quaternion matrix and semi-sensor product theory, the quaternion matrix equation is transformed into its equivalent real matrix equation. Considered the structural characteristics of Hankel matrix, independent elements of the solution matrix are extracted to reconstruct a new solution vector, thus the computational complexity of the problem is reduced. The existing conditions of Hankel solutions of the equation are obtained and the general solutions of the equation are given. Finally, the algorithm finding the solution of the discussed problem is provided.更多还原