In this paper, we investigate an inverse eigenvalue problem for matrices that are obtained from pseudo-Jacobi matrices by only modifying the $(1,r)$-th and $(r,1)$-th entries, $3\le r\le n$. Necessary and sufficient conditions under which the problem is solvable are derived. Uniqueness results are presented and an algorithm to reconstruct the matrices from the given spectral data is proposed. Illustrative examples are provided.

中文翻译：

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修改后的伪Jacobi矩阵的特征值反问题

在本文中，我们研究了通过仅修改伪雅科比矩阵获得的矩阵的特征值反问题 $（\mathrm{1个}，\mathrm{[R}）$-th和 $（\mathrm{[R}，\mathrm{1个}）$-第项， $3\le \mathrm{[R}\le ñ$。得出解决问题的必要和充分条件。给出了唯一性结果，并提出了一种从给定的光谱数据中重构矩阵的算法。提供了说明性示例。