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中文摘要：
称R∈C^m×m为k次轮换矩阵若R的最小多项式为x^k-1（k≥）,令μ∈{0,1,…，k-1}和ζ=e2πi/k.若R∈C^m×m和S∈C^n×n为k次轮换矩阵，则称A∈C^m×n为（R,S,μ）对称矩阵若RAS^-1=ζμA.本文研究了（R，S，μ）对称矩阵的逆问题和最佳逼近问题，得到了解的表达式．并讨论了最佳逼近解的扰动分析，得到了比较满意的理论结果，最后通过数值算例验证了该理论结果的正确性．
英文摘要：
A matrix R∈C^n×n is said to be k-involutary if its minimal polynomial is xk-1 for some k≥2.Let μ∈{0,1….k-1}andζ=e2πi/k.If A∈C^m×m ,S∈C^n×n and R and S are k-involutory, we say that A is （R, S, μ）-symmetric if RAS^-1=ζμA. In this paper we discuss the inverse problem and associated approximation problem for （R, S, μ）-symmetric matrices. Moreover, we provide a perturbation bound for the solution of the approximation problem and present some illustrative experiments to show the correctness of the perturbation bound.
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