摘要
Let P ∈ C^(n×n) be a Hermitian and {k + 1}-potent matrix, i.e., P^(k+1)= P = P~*,where(·)*~stands for the conjugate transpose of a matrix. A matrix X ∈ Cn×nis called{P, k + 1}-reflexive(anti-reflexive) if PXP = X(P XP =-X). The system of matrix equations AX = C, XB = D subject to {P, k + 1}-reflexive and anti-reflexive constraints are studied by converting into two simpler cases: k = 1 and k = 2, the least squares solution and the associated optimal approximation problem are also considered.
Let P ∈ C^（n×n） be a Hermitian and {k ＋ 1}-potent matrix, i.e., P^（k＋1）= P = P~＊,where（·）＊~stands for the conjugate transpose of a matrix. A matrix X ∈ Cn×nis called{P, k ＋ 1}-reflexive（anti-reflexive） if PXP = X（P XP =-X）. The system of matrix equations AX = C, XB = D subject to {P, k ＋ 1}-reflexive and anti-reflexive constraints are studied by converting into two simpler cases： k = 1 and k = 2, the least squares solution and the associated optimal approximation problem are also considered.
基金
Supported by the Education Department Foundation of Hebei Province（QN2015218）
Supported by the Natural Science Foundation of Hebei Province（A2015403050）
