@techreport{fa1a63cf4eb94866a3fb0e0ac5afb723,

title = "Spectral Symmetry in Conference Matrices",

abstract = " A conference matrix of order $n$ is an $n\times n$ matrix $C$ with diagonal entries $0$ and off-diagonal entries $\pm 1$ satisfying $CC^\top=(n-1)I$. If $C$ is symmetric, then $C$ has a symmetric spectrum $\Sigma$ (that is, $\Sigma=-\Sigma$) and eigenvalues $\pm\sqrt{n-1}$. We show that many principal submatrices of $C$ also have symmetric spectrum, which leads to examples of Seidel matrices of graphs (or, equivalently, adjacency matrices of complete signed graphs) with a symmetric spectrum. In addition, we show that some Seidel matrices with symmetric spectrum can be characterized by this construction. ",

keywords = "math.CO, 05C50",

author = "Haemers, {Willem H.} and {Parsaei Majd}, Leila",

year = "2020",

month = apr,

day = "13",

language = "English",

series = "arXiv",

publisher = "Cornell University Library",

type = "WorkingPaper",

institution = "Cornell University Library",

}