四元数矩阵方程AX=B的实部半正定解(英文)

The Re-Positive Semidefinite Solution to the Quaternion Matrix Equation AX=B

一个ｎ×ｎ实四元数矩阵称为实部半正定（或正定）矩阵，如果对于任意的非零ｎ维四元数列向量ｘ，有Ｒｅ［ｘＡｘ］≥０（或＞０）．本文给出了四元数矩阵方程ＡＸ＝Ｂ有实部半正定（或正定）矩阵解的充要条件及其通解的表达式。

An n×n real quaternion matrix A is termed Re-psd (or Rd-pd) if the real part of x*AX is nonnegative (or positive) for every nonzero quaternion nvecotr x. The necessary and sufficient condition for the existence of and the expression for Re-psd(Re-pd) solution of the linear matrix equation AX=B over the quaternion field are derived. In addidon, a criterion for a partitioned n×n quaternion matrix is Re-psd(or Re-pd) is presented.