| Abstrakt: |
Abstract: An n × n sign pattern A is said to be potentially nilpotent if there exists a nilpotent real matrix B with the same sign pattern as A. Let D_{n,r} be an n × n sign pattern with 2 \geqslant r \geqslant n such that the superdiagonal and the (n, n) entries are positive, the (i, 1) (i = 1,..., r) and (i, i − r + 1) (i = r + 1,..., n) entries are negative, and zeros elsewhere. We prove that for r \geqslant 3 and n \geqslant 4r − 2, the sign pattern D_{n,r} is not potentially nilpotent, and so not spectrally arbitrary. |
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