We investigate an inverse eigenvalue problem for constructing a special kind of acyclic matrices. The problem involves the reconstruction of the matrices whose graph is an m -centipede. This is done by using the (2 m − 1)st and (2 m )th eigenpairs of their leading principal submatrices. To solve this problem, the recurrence relations between leading principal submatrices are used.

中文翻译：

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构造一种具有两个特征对的无环矩阵的特征值反问题

我们研究了构造一种特殊类型的非循环矩阵的特征值反问题。这个问题涉及到矩阵的重建，其图是一个 m -蜈蚣。这是通过使用它们的主要主子矩阵的第 (2 m - 1) 个和第 (2 m ) 个特征对来完成的。为了解决这个问题，使用了前导主子矩阵之间的递推关系。