线性矩阵方程的斜,Hermit{P,k+1},Hamilton解

摘要 给定矩阵，P∈ Cn×n且P*=-P=Pk+1.考虑了矩阵方程，AX=B存在斜Hermite{P，k+1}（斜）Hamilton解的充要条件，并给出了解的表达式.进一步，对于任意给定的矩阵？∈ Cn×n，给出了使得Frobenius范数||？-ā||取得最小值的最佳逼近解ā∈ Cn×n.当矩阵方程，AX=B，不相容时，给出了斜，Hermite{P，k+1}（斜）Hamilton最小二乘解，在此条件下，给出了对于任意给定矩阵的最佳逼近解.最后给出一些数值实例.
Abstract：Given P ∈Cn×n and P*=-P=P k+1, we consider the necessary and sufficient conditions such that the matrix equation AX=B is consistent with the skew-Hermitian {P, k + 1} (skew-) Hamiltonian structural constraint. Then, the corresponding expressions of the constraint solutions are also obtained. For any given matrix ？ ∈ Cn×n, we present the optimal approximate solution ā ∈ Cn×n such that ||？-ā|| is minimized in the Frobenius norm sense. If the matrix equation AX=B is not consistent, its least-squares skew-Hermitian {P, k + 1} (skew-) Hamiltonian solutions are given. Under the least-square sense, we consider the best approximate solutions to any given matrix. Finally, some illustrative experiments are also presented.