Nonnegative realizability with Jordan structure

A general method is given for merging blocks in the Jordan canonical form of a nonnegative matrix. As a consequence, results, more general than any prior ones, are given for the universal realizability of spectra, that is, spectra which are realizable by a nonnegative matrix for each possible Jordan canonical form allowed by the spectrum. In particular, we generalize a classical result due to Minc, regarding positive diagonalizable matrices. For example, any spectrum that is diagonalizably realizable by a nonnegative matrix with mostly positive off-diagonal entries is universally realizable.