关于四元数矩阵方程AX＝B

On the Quaternion Matrix Equation AX=B

本文定义了四元数体Ω上亚半正定矩阵，给出了Ω上矩阵方程ＡＸ＝Ｂ有亚（半）正定解和西矩阵解的充要条件及其解集结构．

Metapositive semidefinite quaternion matrix is defined, and necessary and sufficient conditions for the existence of and the expressions for metapositive (semi)-definite solutions and unitary solutions of the quaternioo matrix equation AX=B are derived.