TY  - JOUR
ID  - Lindner2018
LB  - Lindner2018
AU  - Lindner, Marko
TI  - Circulant matrices: norm, powers, and positivity
ST  - Circulant matrices: norm, powers, and positivity
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2018
VL  - 38
IS  - 6
SP  - 849
EP  - 857
DO  - https://doi.org/10.7494/OpMath.2018.38.6.849
UR  - https://doi.org/10.7494/OpMath.2018.38.6.849
AB  - 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.
KW  - spectral norm
KW  - circulant matrix
KW  - eventually positive semigroups
SN  - 1232-9274
ER  -