Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6416452 | Linear Algebra and its Applications | 2014 | 11 Pages |
Abstract
We prove a general theorem that gives tight bounds on the spectral norms of triangularly truncated k-Fibonacci and k-Lucas circulant matrices. The bounds are good enough to enable the calculation of the limitâCââÏ(C)â, as the dimension n approaches infinity, where Ï(C) denotes the triangular truncation of C, and C is any nÃn circulant matrix built using a sequence (si) satisfyingsi=ksiâ1+siâ2. In particular, we have that this limit is equal to the golden ratio, if C is built using either the ordinary Fibonacci or Lucas sequence.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
John Dixon, Michael Goldenberg, Ben Mathes, Justin Sukiennik,