方程组AX=B与XC=D的(反)自反酉约束解  

The reflexive and anti-reflexive unitary solutions to matrix equations AX=B and XC=D

作　　者：史雅萍 刘喜富 SHI Yaping;LIU Xifu(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《内江师范学院学报》2024年第4期26-31,44,共7页Journal of Neijiang Normal University

基　　金：重庆市自然科学基金项目(cstc2021jcyj-msxmX0195,CSTB2022NSCQ-MSX0896);重庆市教委科技项目(KJQN202100505,KJQN202200512)。

摘　　要：对于给定广义反射矩阵P,研究了矩阵方程组AX=B与XC=D在关于广义反射矩阵P(反)自反酉约束下的约束解,并通过矩阵的奇异值分解与Hermite矩阵的谱分解得到了该问题的解的显式表达式.最后用数值算例验证了结论的正确性.For a given generalized reflection matrix P,the reflexive and anti-reflexive unitary solutions to matrix equations AX=B and XC=D with respect to generalized reflection matrix P are investigated.By using singular value decomposition and spectral decomposition of symmetric matrix,the explicit expressions for the constraint solutions mentioned above are obtained.Finally,numerical examples are presented to illustrate and explain our results.

关 键 词：约束解 谱分解 奇异值分解 (反)自反矩阵 酉矩阵 

分 类 号：O241.6[理学—计算数学]