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

A note on Fibonacci matrices of even degree

Michele Elia

 Dipartimento di Elettronica, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino I-10129, Italy
Received 1 March 2001

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.