Sign Patterns of Inverse Doubly-Nonnegative Matrices
arXiv:1903.04141 · doi:10.1016/j.laa.2020.10.005
Abstract
The sign patterns of inverse doubly-nonnegative matrices are examined. A necessary and sufficient condition is developed for a sign matrix to correspond to an inverse doubly-nonnegative matrix. In addition, for a doubly-nonnegative matrix whose graph is a tree, the inverse is shown to have a unique sign pattern, which can be expressed in terms of a two-coloring of the graph.
Final version of paper, appeared in Linear Algebra and its Applications in March 2021