Least-norm and Extremal Ranks of the Least Square Solution to the Quaternion Matrix Equation AXB = C Subject to Two Equations
In this paper, we give the expression of the least square solution of the linear quaternion matrix equation AXB = C subject to a consistent system of quaternion matrix equations D1X = F1, XE2 =F2, and derive the maximal and minimal ranks and the leastnorm of the above mentioned solution. The finding...
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| Published in | Algebra colloquium Vol. 21; no. 3; pp. 449 - 460 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Singapore
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and Suzhou University
01.09.2014
World Scientific Publishing Co. Pte., Ltd |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1005-3867 0219-1733 |
| DOI | 10.1142/S100538671400039X |
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| Abstract | In this paper, we give the expression of the least square solution of the linear quaternion matrix equation AXB = C subject to a consistent system of quaternion matrix equations D1X = F1, XE2 =F2, and derive the maximal and minimal ranks and the leastnorm of the above mentioned solution. The finding of this paper extends some known results in the literature. |
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| AbstractList | In this paper, we give the expression of the least square solution of the linear quaternion matrix equation AXB=C subject to a consistent system of quaternion matrix equations D1X=F1, XE2=F2, and derive the maximal and minimal ranks and the least-norm of the above mentioned solution. The finding of this paper extends some known results in the literature. In this paper, we give the expression of the least square solution of the linear quaternion matrix equation AXB = C subject to a consistent system of quaternion matrix equations D1X = F1, XE2 =F2, and derive the maximal and minimal ranks and the leastnorm of the above mentioned solution. The finding of this paper extends some known results in the literature. In this paper, we give the expression of the least square solution of the linear quaternion matrix equation AXB=C subject to a consistent system of quaternion matrix equations D 1 X=F 1 , XE 2 =F 2 , and derive the maximal and minimal ranks and the least-norm of the above mentioned solution. The finding of this paper extends some known results in the literature. |
| Author | Yubao Bao |
| AuthorAffiliation | School of Mathematics, Shandong Normal University Jinan, Shandong 250014, China |
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| Notes | In this paper, we give the expression of the least square solution of the linear quaternion matrix equation AXB = C subject to a consistent system of quaternion matrix equations D1X = F1, XE2 =F2, and derive the maximal and minimal ranks and the leastnorm of the above mentioned solution. The finding of this paper extends some known results in the literature. 11-3382/O1 quaternion matrix equation, maximal rank, minimal rank, least square solu-tion, least-norm Yubao Bao School of Mathematics, Shandong Normal University Jinan, Shandong 250014, China E-mail： baoyubaobao@sohu.com ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
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| SubjectTerms | Least squares Mathematical analysis Matrix methods Quaternions 四元数矩阵方程 最小二乘解 极值 溶液 线性矩阵方程 |
| Title | Least-norm and Extremal Ranks of the Least Square Solution to the Quaternion Matrix Equation AXB = C Subject to Two Equations |
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