@Article{NM-15-312, author = {J. P. Liang and M. He }, title = {The totally non-positive matrix completion problem}, journal = {Numerical Mathematics, a Journal of Chinese Universities}, year = {2006}, volume = {15}, number = {4}, pages = {312--319}, abstract = { In this paper, the totally non-positive matrix is introduced. The totally non-positive completion asks which partial totally non-positive matrices have a completion to a totally non-positive matrix. This problem has, in general, a negative answer. Therefore, our question is for what kind of labeled graphs $G$ each partial totally non-positive matrix whose associated graph is $G$ has a totally non-positive completion? If $G$ is not a monotonically labeled graph or monotonically labeled cycle, we give necessary and sufficient conditions that guarantee the existence of the desired completion. }, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/nm/8039.html} }