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The work in this paper was motivated by [3], where Eschenbach and Li listed four 4 by 4 sign patterns, conjectured to be nilpotent sign patterns of nilpotence index at least 3. These sign patterns with no zero entries, called full sign patterns, are shown to be potentially nilpotent of nilpotence index 3. We also generalize these sign patterns of order 4 so that we provide classes of n by n sign patterns of nilpotence indices at least 3, if they are potentially nilpotent. Furthermore it is shown that if a full sign pattern A of order n has nilpotence index k with 2≤k≤n − 1, then sign pattern A has nilpotent realizations of nilpotence indices k, k + 1, . . . , n. Hence, the four 4 by 4 sign patterns in [3, page 91] also allow nilpotent realizations of nilpotence index 4.
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참고문헌 (5)
참고문헌 신청
C. A. Eschenbach / 1999 / Potentially nilpotent sign pattern matrices / Linear Algebra and its Applications 299 : 81 ~ 99
I.-J. Kim / 2009 / Generating potentially nilpotent full sign patterns / Electronic Journal of Linear Algebra 18 : 162 ~ 175
M. S. Cavers / 2005 / Spectrally and inertially arbitrary sign patterns / Linear Algebra and its Applications 394 : 53 ~ 72
R. A. Brualdi / 1995 / Matrices of Sign-solvable Linear Systems / Cambridge University Press
Y. Gao / 2007 / Sign patterns allowing nilpotence of index 3 / Linear Algebra and its Applications 424 : 55 ~ 70
I.-J. Kim / 2009 / Generating potentially nilpotent full sign patterns / Electronic Journal of Linear Algebra 18 : 162 ~ 175
M. S. Cavers / 2005 / Spectrally and inertially arbitrary sign patterns / Linear Algebra and its Applications 394 : 53 ~ 72
R. A. Brualdi / 1995 / Matrices of Sign-solvable Linear Systems / Cambridge University Press
Y. Gao / 2007 / Sign patterns allowing nilpotence of index 3 / Linear Algebra and its Applications 424 : 55 ~ 70
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