四元数矩阵方程AX=B的实部半正定解(英文) |
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引用本文: | 王卿文,姜同松,林春艳. 四元数矩阵方程AX=B的实部半正定解(英文)[J]. 大学数学, 1997, 0(2) |
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作者姓名: | 王卿文 姜同松 林春艳 |
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作者单位: | 山东昌潍师专数学系(王卿文),山东临沂师专数学系(姜同松),山东财政学院(林春艳) |
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摘 要: | 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,并给出了四元数分块阵为实部半正定(或正定)矩阵的一个判别法则
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关 键 词: | 矩阵方程,四元数体,实部半正定矩阵 |
The Re-Positive Semidefinite Solution to the Quaternion Matrix Equation AX=B |
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Abstract: | 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. |
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Keywords: | matrix equation the quaternion field Re-Positive semidefinite matrix. |
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