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Mathematics > Functional Analysis

arXiv:1803.09526 (math)
[Submitted on 26 Mar 2018 (v1), last revised 23 Apr 2018 (this version, v2)]

Title:Circulant matrices: norm, powers, and positivity

Authors: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.
Subjects: Functional Analysis (math.FA)
MSC classes: 15A60, 15B05, 15B48
Cite as: arXiv:1803.09526 [math.FA]
  (or arXiv:1803.09526v2 [math.FA] for this version)
  https://doi.org/10.48550/arXiv.1803.09526

Submission history

From: Marko Lindner [view email]
[v1] Mon, 26 Mar 2018 11:50:27 UTC (10 KB)
[v2] Mon, 23 Apr 2018 19:25:28 UTC (10 KB)
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