Circulant matrices: norm, powers, and positivity

Opuscula Mathematica

Marko Lindner¹ 

关键词: spectral norm;    circulant matrix;    eventually positive semigroups;   

DOI  :  10.7494/OpMath.2018.38.6.849

学科分类：数学（综合）

来源: AGH University of Science and Technology Press

【 摘 要 】

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.

【 授权许可】

Free