Spectrally and inertially arbitrary sign patterns (Q1765887)

This paper gives sign patterns generalizing those of \textit{Y. Gao} and \textit{Y. Shao} [Linear Multilinear Algebra 49, No. 2, 161-168 (2001; Zbl 0993.15009)], and of \textit{Z. Miao} and \textit{J. Li} [Linear Algebra Appl. 357, No. 1--3, 133--141 (2002; Zbl 1015.05019)], which are spectrally arbitrary, that is, an \(n\times n\) matrix with one of these sign patterns can have any multiset of \(n\) complex numbers which is conjugation invariant, as its spectrum. It characterizes \(3\times 3\) spectrally arbitrary and inertially arbitrary sign patterns.