| 一个四元数矩阵方程的可解性 |
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| 引用本文： | 曹文胜.一个四元数矩阵方程的可解性[J].高校应用数学学报(英文版),2002,17(4):490-498. |
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| 作者姓名： | 曹文胜 |
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| 作者单位： | Cao WenshengInstitute of Math.，Xiangtan Polytechnic Univ.，Xiangtan 411201，China. |
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| 基金项目： | the National Natural Science Foundation of China(1980 10 11) |
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| 摘 要： | § 1 IntroductionL et R be the real number field,C=R Ri be the complex numberfield,and H=C Cj=R Ri Rj Rk be the quaternion division ring over R,where k:=ij=- ji,i2 =j2 =k2 =- 1 .Ifα=a1 +a2 i+a3 j+a4 k∈ H ,where ai∈ R,then letα=a1 - a2 i- a3 j- a4 k bethe conjugate ofα.L et Hm× nbe the setof all m× n matrices over H.If A=(aij)∈ Hn× n ,L etATbe the transpose matrix of A,A be the conjugate matrix of A,and A* =(aij) T be thetranspose conjugate matrix of A.A∈Hn× nis said…
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| 关 键 词： | 矩阵方程 可解性 四元数 常规解法 |
| 收稿时间： | 17 September 2001 |
Solvability of a quaternion matrix equation |
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| Wensheng Cao.Solvability of a quaternion matrix equation[J].Applied Mathematics A Journal of Chinese Universities,2002,17(4):490-498. |
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| Authors: | Wensheng Cao |
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| Institution: | (1) Institute of Math., Xiangtan Polytechnic Univ., 411201 Xiangtan, China |
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| Abstract: | This paper discusses the solvability of quaternion matrix equation A*X*B* ± B X A=D and obtains it’s general explicit solutions in terms of A,B,D and their Moore-Penrose inverses.
Supported by the National Natural Science Foundation of China (19801011). |
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| Keywords: | Moore Penrose inverse quaternion matrix Hermite matrix |
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