NEW APPROACH TO THE SIGN PATTERNS THAT REQUIRE POWER NONNEGATIVITY, OR REQUIRE EVENTUAL NONNEGATIVITY
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A sign pattern matrix A is called a powerful sign pattern matrix if Ak does not contain an ambiguous entry for all positive inte- ger k. In this paper, we classify the irreducible powerful sign patterns, and prove that irreducible sign pattern matrices that require power- nonnegativity or require eventual nonnegativity are powerful sign pat- terns. We also characterized the reducible sign pattern matrices that require eventual nonnegativity.
Abstract
A sign pattern matrix A is called a powerful sign pattern matrix if Ak does not contain an ambiguous entry for all positive inte- ger k. In this paper, we classify the irreducible powerful sign patterns, and prove that irreducible sign pattern matrices that require power- nonnegativity or require eventual nonnegativity are powerful sign pat- terns. We also characterized the reducible sign pattern matrices that require eventual nonnegativity.
참고문헌 (8)
- M. Catral, "Sign patterns that require or allow power-positivity", lectronic Journal of Linear Algebra, 19, pp.121~128 (2010)
- E. M. Ellison, "Sign patterns that require eventual positivity or require eventual nonnegativity", Electronic Journal of Linear Algebra, 19, pp.98~107 (2010)
- G. M. Engel, "Cyclic and diagonal product on a matrix", Linear Algebra Appl, 7, pp.301~335 (1973)
- C. A. Eschenbach, "Self-inverse sign patterns", IMA Vol. Math. Appl., 190, pp.169~179 (1993)
- C. A. Eschenbach, "The graph of the unambiguous entries in the product of two (+,-) sign pattern matrices", Linear Algebra Appl, 260, pp.95~118 (1997)
- Z. Li, F. Frank, "On the period and base of a sing pattern matrix", Linear Algebra Appl., 212(213), pp.101~120 (1994)
- H. Minc, "Nonnegative matrices" (1988), Wiley
- J. Stuart, "Irreducible sign k-potent sign pattern matrices", Linear Algebra Appl, 294, pp.85~92 (1999)