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Keywords:
spectrally arbitrary sign pattern; $2n$-conjecture
spectrally arbitrary sign pattern; $2n$-conjecture
Summary:
We develop a geometric method for studying the spectral arbitrariness of a given sign pattern matrix. The method also provides a computational way of computing matrix realizations for a given characteristic polynomial. We also provide a partial answer to $2n$-conjecture. We determine that the $2n$-conjecture holds for the class of spectrally arbitrary patterns that have a column or row with at least $n-1$ nonzero entries.
References:
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