一四元数矩阵方程解的研究

INVESTIGATION OF THE SOLUTION TO A QUATERNION MATRIX EQUATION

摘要在四元数体上用矩阵秩的方法研究了矩阵方程的Hermitian解，得到了一个矩阵方程的Hermitian解能够分鳃成两个矩阵方程Hermitian解和的充分必要条件．利用和分解的关系式推导出四元数矩阵Hermitian广义逆等式成立的充要条件．

By using methods of rank for matrix, we investigate Hermitian solution to the matrix equation over quaternion algebra. We give some necessary and sufficient conditions for Hermitian solution of one matrix equation to decompose the sum of Hermitian solutions of the other two matrix equations. We also present necessary and sufficient conditions of Hermitian generalized inverse equalities by the additive decompositions.