Geodesic
A geometric construction for spectrally arbitrary sign pattern matrices and the $2n$-conjecture
Czechoslovak Mathematical Journal, Tome 73 (2023) no. 2, pp. 565-580
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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.
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.
DOI : 10.21136/CMJ.2023.0132-22
Classification : 15B35
Keywords: spectrally arbitrary sign pattern; $2n$-conjecture 
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Jadhav, Dipak; Deore, Rajendra. A geometric construction for spectrally arbitrary sign pattern matrices and the $2n$-conjecture. Czechoslovak Mathematical Journal, Tome 73 (2023) no. 2, pp. 565-580. doi: 10.21136/CMJ.2023.0132-22

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