Extremal ranks of the solution to a system of real quaternion matrix equations 被引量：1

Extremal ranks of the solution to a system of real quaternion matrix equations

下载PDF

导出

摘要 In this paper, the maximal and minimal ranks of the solution to a system of matrix equations over H, the real quaternion algebra, were derived. A previous known result could be regarded as a special case of the new result. In this paper, the maximal and minimal ranks of the solution to a system of matrix equations over H, the real quaternion algebra, were derived. A previous known result could be regarded as a special case of the new result.

作者俞绍文王卿文

机构地区 Department of Mathematics

出处《Journal of Shanghai University(English Edition)》 CAS 2007年第3期229-232,共4页 上海大学学报（英文版）

基金 Project supported by the National Natural Science Foundation of China （Grant No.60672160）

关键词 system of matrix equations SOLUTION minimal rank maximal rank generalized inverse system of matrix equations, solution, minimal rank, maximal rank, generalized inverse

分类号 O15 [理学—基础数学]

引文网络
相关文献

参考文献1

1QingWenWANG.A System of Four Matrix Equations over von Neumann Regular Rings and Its Applications[J].Acta Mathematica Sinica,English Series,2005,21(2):323-334. 被引量：9

二级参考文献24

1Wang, Q. W., Li, S. Z.: The persymmetric and perskewsymmetric solutions to sets of matrix equations over a finite central algebra. Acta Math Sinica, Chinese Serges, 47(1), 27-34 (2004).
2Wang, Q. W.: A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity. Linear Alqebra Appl., 384, 43-54 (2004).
3Bhimasankaram, P.: Common solutions to the linear matrix equations AX=B, CX=D, and EXF=G.Sankhya Ser. A, 38, 404-409 (1976).
4Aitken, A. C.: Determinants and Matrices, Oliver and Boyd, Edinburgh, 1939.
5Datta, L., Morgera, S. D.: On the reducibility of centrosymmetric matrices-applications in engineering problems. Circuits Systems Siq. Proc., 8(1), 71-96 (1989).
6Cantoni, A., Butler, P.: Eigenvalues and eigenvectors of symmetric centrosymmetric matrices. Linear Algebra Appl., 13, 275-288 (1976).
7Weaver, J. R.: Centrosymmetric (cross-symmetric) matrices, their basic properties, eigenvalues, eigenvectors. Amer. Math. Monthly, 92, 711-717 (1985).
8Lee, A.: Centrohermitian and skew-centrohermitian matrices. Linear Algebra Appl., 29, 205-210 (1980).
9Hell, R. D., Bates, R. G., Waters, S. R.: On centrohermitian matrices. SIAM J. Matrix Anal. Appl., 11(1),128-133 (1990).
10Hell, R. D., Bates, R. G., Waters, S. R.: On perhermitian matrices. SIAM J. Matrix Anal. Appl., 11(2),173-179 (1990).

共引文献8

1谢仲洲,刘晓冀.一类四元数体上线性矩阵方程组的解[J].四川师范大学学报（自然科学版）,2009,32(4):439-442. 被引量：2
2WANG QingWen,van der WOUDE J. W.,YU ShaoWen.An equivalence canonical form of a matrix triplet over an arbitrary division ring with applications[J].Science China Mathematics,2011,54(5):907-924. 被引量：4
3Qing-wen Wang Yan Zhou Qin Zhang.Ranks of the Common Solution to Six Quaternion Matrix Equations[J].Acta Mathematicae Applicatae Sinica,2011,27(3):443-462. 被引量：3
4宋彩芹,陈果良,王晓东.ON SOLUTIONS OF QUATERNION MATRIX EQUATIONS XF-AX=BY AND XF-A=BY[J].Acta Mathematica Scientia,2012,32(5):1967-1982.
5连德忠.一类四元数矩阵三次方程的可解性(英文)[J].数学研究,2012,45(4):390-403.
6Masoud Hajarian.Efcient Iterative Solutions to General Coupled Matrix Equations[J].International Journal of Automation and computing,2013,10(5):481-486.
7柯艺芬,马昌凤.一类矩阵方程组的反对称-正交对称解[J].福建师范大学学报（自然科学版）,2015,31(1):12-17. 被引量：2
8彭卓华.子矩阵约束下矩阵方程组的双对称最小二乘解[J].数学物理学报（A辑）,2015,35(1):131-150. 被引量：3

同被引文献4

1张凤霞.不等式约束下AXA~＊=B的Hermite最小二乘解[J].上海理工大学学报,2012,34(3):284-288. 被引量：1
2林冠军.矩阵乘积的加权广义逆的混合反序律[J].泉州师范学院学报,2013,31(2):20-24. 被引量：1
3肖庆丰,胡锡炎,张磊.秩约束下矩阵方程AX=B的反对称解及其最佳逼近(英文)[J].数学杂志,2013,33(5):803-810. 被引量：5
4HE Zhuo-heng,WANG Qing-wen.A Pair of Mixed Generalized Sylvester Matrix Equations[J].上海大学学报（自然科学版）,2014,20(2):138-156. 被引量：4

引证文献1

1查秀秀,李莹,王方圆.具有特殊结构的最小二乘广义逆[J].聊城大学学报（自然科学版）,2015,28(1):10-14.

1Chunyan Lin.Ranks of Submatrices in a Solution to a Consistent System of Linear Quaternion Matrix Equations with Applications[J].Algebra Colloquium,2014,21(3):399-410.
2Yubao Bao.Least-norm and Extremal Ranks of the Least Square Solution to the Quaternion Matrix Equation AXB = C Subject to Two Equations[J].Algebra Colloquium,2014,21(3):449-460. 被引量：1
3Qing-wen Wang Yan Zhou Qin Zhang.Ranks of the Common Solution to Six Quaternion Matrix Equations[J].Acta Mathematicae Applicatae Sinica,2011,27(3):443-462. 被引量：3
4Zhuoheng He,Qingwen Wang.A System of Periodic Discrete-time Coupled Sylvester Quaternion Matrix Equations[J].Algebra Colloquium,2017,24(1):169-180. 被引量：1
5宋彩芹,陈果良,王晓东.ON SOLUTIONS OF QUATERNION MATRIX EQUATIONS XF-AX=BY AND XF-A=BY[J].Acta Mathematica Scientia,2012,32(5):1967-1982.
6Tong Song JIANG,Mu Sheng WEI.On a Solution of the Quaternion Matrix Equation X-A B=C and Its Application[J].Acta Mathematica Sinica,English Series,2005,21(3):483-490. 被引量：3
7Cao WenshengInstitute of Math.,Xiangtan Polytechnic Univ.,Xiangtan 411201,China..SOLVABILITY OF A QUATERNION MATRIX EQUATION[J].Applied Mathematics(A Journal of Chinese Universities),2002,17(4):490-498. 被引量：3
8薛有才.The Least Square Solutions to the Quaternion Matrix Equation AX=B[J].Chinese Quarterly Journal of Mathematics,1997,12(1):87-90. 被引量：3
9WANG BaoShan,ZHANG ZhiKai.The p-local ranks of finite simple groups with abelian Sylow p-subgroups[J].Science China Mathematics,2011,54(2):341-350.
10陈焕艮.On Projective Modules with Constant Ranks[J].Chinese Quarterly Journal of Mathematics,1996,11(3):74-78.

Journal of Shanghai University(English Edition)

2007年第3期

浏览历史

内容加载中请稍等...