Functions Preserving Nonnegativity of Matrices

@article{Bharali2008FunctionsPN,
  title={Functions Preserving Nonnegativity of Matrices},
  author={Gautam Bharali and Olga Holtz},
  journal={SIAM J. Matrix Anal. Appl.},
  year={2008},
  volume={30},
  pages={84-101}
}
The main goal of this work is to determine which entire functions preserve nonnegativity of matrices of a fixed order $n$—i.e., to characterize entire functions $f$ with the property that $f(A)$ is entrywise nonnegative for every entrywise nonnegative matrix $A$ of size $n\times n$. Toward this goal, we present a complete characterization of functions preserving nonnegativity of (block) upper-triangular matrices and those preserving nonnegativity of circulant matrices. We also derive necessary… 

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