论文标题
某些BRAUER和RADO的作用导致非负相对频谱问题
The role of certain Brauer and Rado results in the nonnegative inverse spectral problems
论文作者
论文摘要
我们说，如果它是非负矩阵$ a $（实现的矩阵），则可以实现$λ= \ {λ__{1}，\ ldots，λ_{n} \} $。我们说，如果$λ$对于$λ允许的每种可能的约旦规范形式都可以实现，则可以普遍实现。$此工作不包含新的结果。正如其标题所示，我们的目标是在研究非负相对频谱问题的研究中显示和强调Brauer和Rado的某些结果的相关性。我们表明，几乎所有已知的结果为列表提供了足够的条件$λ$，以实现或普遍可实现，可以从Brauer或rado的结果中获得。此外，在这种情况下，我们可能总是计算一个实现矩阵。
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.
