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| 1 | A system of matrix equations and its applications显示文摘We derive the solvability conditions and an expression of the general solution to the system of matrix equations A 1X=C1 , A2Y=C2 , YB2=D2 , Y=Y*, A3Z=C3 , ZB3=D3 , Z=Z*, B4X+(B4X)+C4YC4*+D4ZD4*=A4 . Moreover, we investigate the maximal and minimal ranks and inertias of Y and Z in the above system of matrix equations. As a special case of the results, we solve the problem proposed in Farid, Moslehian, Wang and Wu's recent paper (Farid F O, Moslehian M S, Wang Q W, et al. On the Hermitian solutions to a system of adjointable operator equations. Linear Algebra Appl, 2012, 437: 1854-1891). | WANG QingWen HE ZhuoHeng | 2013 | Science China Mathematics2013，56，9： | 4 |
| 2 | A System of Periodic Discrete-time Coupled Sylvester Quaternion Matrix Equations显示文摘我们为周期的分离时间的联合 Sylvester 矩阵方程 AkXk 的系统在这份报纸导出必要、足够的条件?+? YkBk ? =?Mk ,? CkXk+1 ?+? YkDk ? =?Nk ?( k ?=? 1 ,? 2 )在以等级一致并且概括系数矩阵的逆的四元数代数学上。当它是可解决的时,我们也给系统的一般答案的一个表达式。这份报纸的调查结果在文学概括一些已知的结果。 | Zhuoheng He Qingwen Wang | 2017 | Algebra Colloquium2017，24，1： | 0 |
| 3 | ON SOLUTIONS OF QUATERNION MATRIX EQUATIONS XF-AX=BY AND XF-A=BY显示文摘In this paper,the quaternion matrix equations XF-AX=BY and XF-A=BY are investigated.For convenience,they were called generalized Sylvesterquaternion matrix equation and generalized Sylvester-j-conjugate quaternion matrix equation,which include the Sylvester matrix equation and Lyapunov matrix equation as special cases.By applying of Kronecker map and complex representation of a quaternion matrix,the sufficient conditions to compute the solution can be given and the expressions of the explicit solutions to the above two quaternion matrix equations XF-AX=BY and XF-A=BY are also obtained.By the established expressions,it is easy to compute the solution of the quaternion matrix equation in the above two forms.In addition,two practical algorithms for these two quaternion matrix equations are give.One is complex representation matrix method and the other is a direct algorithm by the given expression.Furthermore,two illustrative examples are proposed to show the efficiency of the given method. | 宋彩芹 陈果良 王晓东 | 2012 | Acta Mathematica Scientia2012，32，5： | 0 |
| 4 | 一个四元数矩阵方程组的η-Hermitian解显示文摘对于四元数矩阵方程组AXA^(η*)+BY B^(η*)=E,CYC^(η*)+DZD^(η*)=F,首先运用4个矩阵的奇异值分解,给出四元数矩阵方程组有η-Hermitian解的充要条件;然后,利用该充要条件给出矩阵方程组η-Hermitian解的表达式. | 陈笛 吴维峰 | 2013 | 上海大学学报(自然科学版)2013，19，6： | 0 |
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