ON NILPOTENCE INDICES OF SIGN PATTERNS

Title & Authors
ON NILPOTENCE INDICES OF SIGN PATTERNS
Erickson, Craig; Kim, In-Jae;

Abstract
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 $\small{2{\leq}k{\leq}n-1}$, then sign pattern A has nilpotent realizations of nilpotence indices k, k + 1, $\small{\ldots}$, n. Hence, the four 4 by 4 sign patterns in [3, page 91] also allow nilpotent realizations of nilpotence index 4.
Keywords
Jordan block;nilpotence index;potentially nilpotent sign pattern;
Language
English
Cited by
1.
Tree sign patterns that allow nilpotence of index 4, Linear and Multilinear Algebra, 2015, 63, 5, 1009
2.
Potentially nilpotent patterns and the Nilpotent-Jacobian method, Linear Algebra and its Applications, 2012, 436, 12, 4433
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