fibonacci.matrix {matrixcalc}R Documentation

Fibonacci Matrix

Description

This function constructs the order n + 1 square Fibonacci matrix which is derived from a Fibonacci sequence.

Usage

fibonacci.matrix(n)

Arguments

n

a positive integer value

Details

Let {f0,  f1,  ,  fn}\left\{ {{f_0},\;{f_1},\; \ldots ,\;{f_n}} \right\} be the set of n+1 n + 1 Fibonacci numbers where f0=f1=1{f_0} = {f_1} = 1 and fj=fj1+fj2,2jn{f_j} = {f_{j - 1}} + {f_{j - 2}},\quad 2 \le j \le n. The order n+1n + 1 Fibonacci matrix F{\bf{F}} has as typical element Fi,j={fij+1ij+100ij+1<0{F_{i,j}} = \left\{ {\begin{array}{cc} {{f_{i - j + 1}}}&{i - j + 1 \ge 0}\\ 0&{i - j + 1 < 0} \end{array}} \right..

Value

An order n+1n + 1 matrix

Note

If the argument n is not a positive integer, the function presents an error message and stops.

Author(s)

Frederick Novomestky fnovomes@poly.edu

References

Zhang, Z. and J. Wang (2006). Bernoulli matrix and its algebraic properties, Discrete Applied Nathematics, 154, 1622-1632.

Examples

F <- fibonacci.matrix( 10 )
print( F )

[Package matrixcalc version 1.0-6 Index]