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International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 8, Pages 457-469
http://dx.doi.org/10.1155/S0161171201006858

A note on Fibonacci matrices of even degree

Dipartimento di Elettronica, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino I-10129, Italy

Received 1 March 2001

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper presents a construction of m-by-m irreducible Fibonacci matrices for any even m. The proposed technique relies on matrix representations of algebraic number fields which are an extension of the golden section field. The explicit construction of some 6-by-6 and 8-by-8 irreducible Fibonacci matrices is given.