Abstract
The work in this paper was motivated by (3), where Eschen- bach 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 nilpo- tence 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 • kn i 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, page91) also allow nilpotent realizations of nilpotence index 4.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
