某些Brauer和Rado结果在非负逆谱问题中的作用
The role of certain Brauer and Rado results in the nonnegative inverse spectral problems
摘要：
我们说一个复数列表$Λ=\{ λ_{1},\ldots ,λ_{n}\}$是可实现的，如果它是一个非负矩阵$A$（实现矩阵）的谱。我们说$Λ$是普遍可实现的，如果它对$ Λ.$所允许的每一种可能的若尔当典范形都是可实现的。正如它的标题说，我们的目标是显示和强调的相关性的某些结果的Brauer和Rado在研究非负逆谱问题。我们表明，几乎所有已知的结果，这给列表$ Λ$是可实现的或普遍可实现的充分条件，可以从Brauer或Rado的结果。此外，在这种情况下，我们总是可以计算一个实现矩阵。
英文摘要：
We say that a list $Λ=\{ λ_{1},\ldots ,λ_{n}\}$ of complex numbers is realizable, if it is the spectrum of a nonnegative matrix $A$ (the realizing matrix). We say that $Λ$ is universally realizable if it is realizable for each possible Jordan canonical form allowed by $ Λ.$ This work does not contain new results. As its title says, our goal is to show and emphasize the relevance of certain results of Brauer and Rado in the study of nonnegative inverse spectral problems. We show that virtually all known results, which give sufficient conditions for the list $ Λ$ to be realizable or universally realizable, can be obtained from the results of Brauer or Rado. Moreover, in this case, we may always compute a realizing matrix.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
