A generalization of tridiagonal matrix determinants, Fibonacci and Lucas numbers (original) (raw)

On Determinants of Some Tridiagonal Matrices Connected with Fibonacci Numbers

International Journal of Pure and Apllied Mathematics, 2013

We will overview some facts about the Fibonacci numbers, Hessenberg matrices and tridiagonal matrices. We will summarize the results on determinants of families of tridiagonal matrices which are equal to a Fibonacci number, but we prove most of this results by simpler and more direct way with the help of The On-line Encyclopedai of Integer Sequences (OEIS).

A generalization of Fibonacci and Lucas matrices

Discrete Applied Mathematics, 2008

We define the matrix U (a,b,s) n of type s, whose elements are defined by the general second-order non-degenerated sequence and introduce the notion of the generalized Fibonacci matrix F (a,b,s) n , whose nonzero elements are generalized Fibonacci numbers. We observe two regular cases of these matrices (s = 0 and s = 1). Generalized Fibonacci matrices in certain cases give the usual Fibonacci matrix and the Lucas matrix. Inverse of the matrix U (a,b,s) n is derived. In partial case we get the inverse of the generalized Fibonacci matrix F

Two determinants with Fibonacci and Lucas entries

Applied Mathematics and Computation, 2007

In this short note, we study two families of determinants the entries of which are linear functions of Fibonacci or Lucas numbers. The results are rather simple, and the two determinants only differ by a constant.