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Potentially nilpotent sign pattern matrices. (English) Zbl 0941.15012
The authors investigate the property $$N$$ of being nilpotent. They establish several qualitative necessary conditions for patterns to allow $$N$$ in Section 2 “Qualitative conditions for nilpotence”. In Section 3 “Patterns that allow nilpotence of index 2”, they investigate the sign patterns that allow nilpotence of index 2. In particular, they characterize minimum rank one patterns that allow nilpotence of index 2, and they provide several constructions of sign patterns that allow nilpotence of index 2. Section 4 “The 3-by-3 sign patterns that allow $$N$$” is devoted to characterize all 3-by-3 sign patterns that allow $$N$$, and Section 5 “$$C_r$$-cockades” gives some results on $$C_r$$-cockade sign pattern matrices that allow $$N$$ or preclude $$N$$.
Reviewer: Y.Kuo (Knoxville)

##### MSC:
 15B33 Matrices over special rings (quaternions, finite fields, etc.)
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