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A geometric construction for spectrally arbitrary sign pattern matrices and the $2 n$ -conjecture

Dipak Jadhav; Rajendra Deore — 2023

Czechoslovak Mathematical Journal

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 $2 n$ -conjecture. We determine that the $2 n$ -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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A geometric construction for spectrally arbitrary sign pattern matrices and the 2 n -conjecture

A geometric construction for spectrally arbitrary sign pattern matrices and the $2 n$ -conjecture