Tree Sign Patterns Of Small Order That Allow An Eventually Positive Matrix
| Autor: | Ber-Lin Yu, Cui, Jie, Cheng, Hong, Zhengfeng Yu |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: | |
| DOI: | 10.5281/zenodo.1110587 |
| Popis: | A sign pattern is a matrix whose entries belong to the set {+,−, 0}. An n-by-n sign pattern A is said to allow an eventually positive matrix if there exist some real matrices A with the same sign pattern as A and a positive integer k0 such that Ak > 0 for all k ≥ k0. It is well known that identifying and classifying the n-by-n sign patterns that allow an eventually positive matrix are posed as two open problems. In this article, the tree sign patterns of small order that allow an eventually positive matrix are classified completely. {"references":["R. A. Brualdi, H. J. Ryser, Combinatorial Matrix Theory, Cambridge:\nCambridge University Press, 1991.","R. A. Horn, C. R. Johnson, Matrix Analysis, Cambridge: Cambridge\nUniversity Press, 1995.","A. Berman, M. Catral, L. M. Dealba, A. Elhashash, F. Hall,\nL. Hogben, I. J. Kim, D. D. Olesky, P. Tarazaga, M. J. Tsatsomeros,\nP. van den Driessche, Sign patterns that allow eventual positivity,\nElectronic Journal of Linear Algebra 19:108-120, 2010.","B. -L. Yu, T. -Z. Huang, J. Luo, H. B. Hua, Potentially eventually positive\ndouble star sign patterns, Applied Mathematics Letters, 25:1619-1624,\n2012.","B. -L. Yu, T. -Z. Huang, On minimal potentially power-positive sign\npatterns, Operators and Matrices, 6:159-167, 2012.","B. -L. Yu, T. -Z. Huang, C. Hong, D. D. Wang, Eventual positivity of\ntridiagonal sign patterns, Linear and Multilinear Algebra, 62:853-859,\n2014.","M. Archer, M. Catral, C. Erickson, R. Haber, L. Hogben,\nX. Martinez-Rivera, A. Ochoa, Constructions of potentially eventually\npositive sign patterns with reducible positive part, Involve, 4:405-410,\n2011.","E. M. Ellison, L. Hogben, M. J. Tsatsomeros, Sign patterns that require\neventual positivity or require eventual nonnegativity, Electronic Journal\nof Linear Algebra, 19:98-107, 2010."]} |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|