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A contribution to the connections between Fibonacci Numbers and Matrix Theory (1306.2845v1)
Published 6 Jun 2013 in math.HO and math.RA
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 $n \times n$ $(n \geq 3)$ $(0,1)-$ 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.