Circulant matrices: norm, powers, and positivity
Functional Analysis
2018-04-25 v2
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 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 . We then generalize the result to complex circulant matrices.
Keywords
Cite
@article{arxiv.1803.09526,
title = {Circulant matrices: norm, powers, and positivity},
author = {Marko Lindner},
journal= {arXiv preprint arXiv:1803.09526},
year = {2018}
}