The Spectral Norm of a Circulant Matrix

Abstract

Let a, b, p, q be integers and (h n ) defined by h 0 = a, h 1 = b, h n = ph n−1 +qh n−2 , n = 2, 3, . . . . Complementing to certain previously known results, we study the spectral norm of the circulant matrix corresponding to h 0 , . . . , h n−1 .

Circulant matrices: norm, powers, and positivity

“…This sufficient condition for membership in C n or C ′ n seems quite generous. [2] suggests the following improvement. Put…”

“…Motivated by studies of so-called Horadam or Fibonacci circulant matrices, the authors of [2,3] ask in [2] under which conditions the spectral norm of C x equals |x 0 + x 1 + · · · + x n−1 |. We give a sufficient and a necessary condition.…”