Sign Patterns of Inverse Doubly-Nonnegative Matrices
This is an incremental theoretical result for matrix theory researchers, extending known results on sign patterns to a specific matrix class.
The paper characterizes sign patterns of inverse doubly-nonnegative matrices, providing a necessary and sufficient condition for a sign matrix to be realizable as such an inverse, and shows that for tree graphs the inverse has a unique sign pattern expressible via a two-coloring.
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.