Czechoslovak Mathematical Journal, Vol. 73, No. 2, pp. 565-580, 2023
A geometric construction for spectrally arbitrary sign pattern matrices and the $2n$-conjecture
Dipak Jadhav, Rajendra Deore
Received March 31, 2022. Published online February 2, 2023.
Abstract: 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.
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Affiliations: Dipak Jadhav (corresponding author), Rajendra Deore, Department of Mathematics, Faculty of Science and Technology, University of Mumbai, Ranade Bhavan, Central Salsette Tramway Rd., Kalina Campus, Vidyanagari, Santacruz(E), Mumbai 400 098, M. S. India, e-mail: jadhav.dipak2585@gmail.com, rpdeore@gmail.com
