| 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 \left\{ {{f_0},\;{f_1},\; \ldots ,\;{f_n}} \right\} be the
set of n + 1 Fibonacci numbers where {f_0} = {f_1} = 1
and {f_j} = {f_{j - 1}} + {f_{j - 2}},\quad 2 \le j \le n. The
order n + 1 Fibonacci matrix {\bf{F}} has as typical element
{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 + 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 )