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 à ∈ Cn×n, we present the optimal approximate solution ā ∈ Cn×n such that ||Ã-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.
YONG Jin-jun
,
CHEN Guo-liang
,
XU Wei-ru
. The skew-Hermitian {P,k+1} Hamiltonian solutions of a linear matrix equation[J]. Journal of East China Normal University(Natural Science), 2018
, 2018(4)
: 32
-46,58
.
DOI: 10.3969/j.issn.1000-5641.2018.04.004
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