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arXiv · 1803.09526

Circulant matrices: norm, powers, and positivity

Marko Lindner
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Abstract

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 ${\bf C}$ 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 ${\bf C^\top C}$. We then generalize the result to complex circulant matrices.

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Marko Lindner. 2018-03-26. Circulant matrices: norm, powers, and positivity. https://arxiv.org/abs/1803.09526

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