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Circulant matrices: norm, powers, and positivity

Lindner M.

Opuscula Mathematica

2018

Vol. 38, no. 6

849--857

In their recent paper "The spectral norm of a Horadam circulant matrix", Merikoski, Haukkanen, Mattila and Tossavainen study under which conditions the spectral norm of a general real circulant matrix C equals the modulus of its row/column sum. We improve on their sufficient condition until we have a necessary one. Our results connect the above problem to positivity of sufficiently high powers of the matrix CTC. We then generalize the result to complex circulant matrices.