A Note on Potentially Power-Positive Sign Patterns

Authors: Ber-Lin Yu, Ting-Zhu Huang

Abstract:

In this note, some properties of potentially powerpositive sign patterns are established, and all the potentially powerpositive sign patterns of order ≤ 3 are classified completely.

Keywords: Sign pattern, potentially eventually positive sign pattern, potentially power-positive sign pattern.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1330627

References:

[1] F. Hall, Z. Li, Sign pattern matrices, in: L. Hogben(Ed.), Handbook of Linear Algebra, Chapman & Hall/CRC Press, Boca Ration, 2007.
[2] R. A. Brualdi, H. J. Ryser, Combinatorial Matrix Theory, Cambridge University Press, Cambridge, 1991.
[3] D. Noutsos, On Perron-Frobenius property of matrices having some negative entries, Linear Aglebra Appl., 412(2006) 132-153.
[4] A. Brauer, On the characteristic roots of power-positive matrices, Duke Math. J., 28(1961) 439-445.
[5] E. M. Ellison, L. Hogben, M. J. Tsatsomeros, Sign patterns that require eventual positivity or require eventual nonnegativity, Electron. J. Linear Algebra, 19(2010) 98-107.
[6] A. Berman, M. Catral, L. M. Dealba, A. Elhashash, F. Hall, L. Hogben, I. J. Kim, D. D. Olesky, P. Tarazaga, M. J. Tsatsomeros, P. van den Driessche, Sign patterns that allow eventual positivity, Electron. J. Linear Algebra, 12(2010) 108-120.
[7] M. Catral, L. Hogben, D. D. Olesky, P. van den Driessche, Sign patterns that require or allow power-positivity, Electron. J. Linear Algebra, 19(2010) 121-128.