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 equationsAX=BandXC=D

摘要

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.

Abstract:For a given generalized reflection matrix P, the reflexive and anti-reflexive unitary solutions to matrix equations AX= Band XC= Dwith respect to generalized reflection matrix Pare 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.