Eigenvector-free solutions to AX = B with PX = XP and XH = sX constraints
Eigenvector-free solutions to AX = B with PX = XP and XH = sX constraints
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DOI：
10.1016/j.amc.2010.12.043
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发表时间：
2011-02
期刊：
影响因子：
--
通讯作者：
Y. Qiu;Anding Wang
中科院分区：
文献类型：
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作者：
Y. Qiu;Anding Wang
考虑矩阵方程AX=B，其中P是给定的Hermitian对合矩阵，s=±1.通过对P的特征值分解，将约束问题等价地转化为两个已知的约束问题，并用P的特征向量表示其解.利用矩阵A，B和P生成的乘积的Moore-Penrose广义逆，可以释放所涉及的特征向量，并给出了一般解的无特征向量公式.在相同的约束条件下，将类似的策略应用于方程AX=B，XC=D。
The matrix equation AX=B with PX=XP and XH=sX constraints is considered, where P is a given Hermitian involutory matrix and s=±1. By an eigenvalue decomposition of P, we equivalently transform the constrained problem to two well-known constrained problems and represent the solutions in terms of the eigenvectors of P. Using Moore–Penrose generalized inverses of the products generated by matrices A, B and P, the involved eigenvectors can be released and eigenvector-free formulas of the general solutions are presented. Similar strategy is applied to the equations AX=B, XC=D with the same constraints.