A contribution to the connections between Fibonacci Numbers and Matrix Theory

2013/06/06 by Miriam Farber, Farber, Miriam, Abraham Berman +1
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Graph theory and applications #Matrix Theory and Algorithms #math.HO #math.RA #msc:11B39 #msc:15A09 #msc:15A15 #msc:15B34

paper · pdf · doi:10.48550/arxiv.1306.2845

7 pages, 2 figures

arxiv created 2013/06/06 · arxiv updated 2013/06/13

Abstract

We present a lovely connection between the Fibonacci numbers and the sums of inverses of (0,1)- triangular matrices, namely, a number S is the sum of the entries of the inverse of an n × n (n ≥ 3) (0,1)- triangular matrix iff S is an integer between 2-F_n-1 and 2+F_n-1. Corollaries include Fibonacci identities and a Fibonacci type result on determinants of family of (1,2)-matrices.

Related

• Group inverses of \0,1\-triangular matrices and Fibonacci numbers
• The Filbert Matrix
• Fibonacci identities from Jordan Identities
• Matrix Powers of Column-Justified Pascal Triangles and Fibonacci Sequences
• On the inverse of a Fibonacci number modulo a Fibonacci number being a Fibonacci number