数学季刊 ›› 2018, Vol. 33 ›› Issue (1): 32-42.doi: 10.13371/j.cnki.chin.q.j.m.2018.01.004
摘要: Let P ∈ Cn×n be a Hermitian and {k + 1}-potent matrix, i.e., Pk+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.
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