Volume 15, Issue 4
The totally non-positive matrix completion problem

J. P. Liang & M. He

Numer. Math. J. Chinese Univ. (English Ser.)(English Ser.) 15 (2006), pp. 312-319

Published online: 2006-11

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  • 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.
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@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} }
TY - JOUR T1 - The totally non-positive matrix completion problem AU - J. P. Liang & M. He JO - Numerical Mathematics, a Journal of Chinese Universities VL - 4 SP - 312 EP - 319 PY - 2006 DA - 2006/11 SN - 15 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/nm/8039.html KW - AB - 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.
J. P. Liang & M. He . (1970). The totally non-positive matrix completion problem. Numerical Mathematics, a Journal of Chinese Universities. 15 (4). 312-319. doi:
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