A uniform type inverse spectrum theorem for entrywise nonnegative matrices

Influenced by earlier results of Fiedler [M. Fiedler, Eigenvalues of nonnegative symmetric matrices, Linear Algebra Appl. 9 (1974) 119–142], Wuven [Guo Wuven, Eigenvalues of nonnegative matrices, Linear Algebra Appl. 266 (1997) 261–270] established interesting theorems and posed several natural questions in the inverse spectrum problem for entrywise nonnegative matrices. We answer some of these (of a uniform character) obtaining the sharpest possible results.