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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Bibliographic Details
Published inAlgebra colloquium Vol. 21; no. 3; pp. 449 - 460
Main Author Bao, Yubao
Format Journal Article
LanguageEnglish
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
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
maximal rank
quaternion matrix equation
minimal rank
least-norm
least square solution
Online AccessGet full text
ISSN1005-3867
0219-1733
DOI10.1142/S100538671400039X

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Summary: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.
Bibliography: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
ISSN:1005-3867
0219-1733
DOI:10.1142/S100538671400039X