Paper detail

The role of certain Brauer and Rado results in the nonnegative inverse spectral problems

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.