Inertially arbitrary sign patterns with no nilpotent realization
A family of irreducible sign patterns \(G_{2k+1}\;(k\geq 2)\) is defined and is proved to be initially arbitrary, but not potentially nilpotent; a proof is based on certain realizations, the nilpotent Jacobi method not being available. The paper also derives properties of coefficients of characteristic polynomials with certain fixed inertias. This is used to prove that \(G_5\) and \(G_7\) are minimal arbitrary sign patterns.
scientific article; zbMATH DE number 5132596