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Circulant matrices with orthogonal rows and off-diagonal entries of absolute value $1$

Daniel Uzcátegui Contreras; Dardo Goyeneche; Ondřej Turek; Zuzana Václavíková — 2021

Communications in Mathematics

It is known that a real symmetric circulant matrix with diagonal entries $d \geq 0$ , off-diagonal entries $\pm 1$ and orthogonal rows exists only of order $2 d + 2$ (and trivially of order $1$ ) [Turek and Goyeneche 2019]. In this paper we consider a complex Hermitian analogy of those matrices. That is, we study the existence and construction of Hermitian circulant matrices having orthogonal rows, diagonal entries $d \geq 0$ and any complex entries of absolute value $1$ off the diagonal. As a particular case, we consider matrices whose...

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Circulant matrices with orthogonal rows and off-diagonal entries of absolute value 1

Circulant matrices with orthogonal rows and off-diagonal entries of absolute value $1$