The symmetric stochastic inverse eigenvalue problem (SSIEP) asks which lists of real numbers occur as the spectra of symmetric stochastic matrices. When the cardinality of a list is 4, Kaddoura and Mourad provided a sufficient condition for SSIEP by a mapping and convexity technique. They also conjectured that the sufficient condition is the necessary condition. This study presents the same sufficient condition for SSIEP, but we do it in terms of the list elements. In this way, we provide a different but more straightforward construction of symmetric stochastic matrices for SSIEP compared to those of Kaddoura and Mourad.

中文翻译：

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具有给定谱的 4 x 4 对称随机矩阵的构造

对称随机逆特征值问题 (SSIEP) 询问哪些实数列表作为对称随机矩阵的谱出现。当列表的基数为 4 时，Kaddoura 和 Mourad 通过映射和凸性技术为 SSIEP 提供了充分条件。他们还猜想，充分条件就是必要条件。本研究为 SSIEP 提供了相同的充分条件，但我们是根据列表元素来进行的。通过这种方式，与 Kaddoura 和 Mourad 的矩阵相比，我们为 SSIEP 提供了不同但更直接的对称随机矩阵构造。