Fibonacci Q- Matrix

Author

Eric W. Weisstein
April 8, 2002

This notebook downloaded from http://mathworld.wolfram.com/notebooks/IntegerSequences/FibonacciQ-Matrix.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/FibonacciQ-Matrix.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Code

FibonacciQ[n_]:=Map[Fibonacci,{{n+1,n},{n,n-1}},{1}]

FibonacciQ[n]//MatrixForm//TraditionalForm

FibonacciQ[1]//MatrixForm

MatrixForm/@Table[FibonacciQ[n],{n,6}]

MatrixForm/@Map[Fibonacci,Table[{{n+1,n},{n,n-1}},{n,6}],{1}]

|(Q^n)|=|Q((|)^n)

Det[FibonacciQ[n]]==Det[FibonacciQ[1]]^n//TraditionalForm

FullSimplify[%,n∈Integers]

(Q^(n+1))(Q^n)=(Q^(2n+1))

MatrixForm@FibonacciQ[n+1].MatrixForm@FibonacciQ[n]==FibonacciQ[2n+1]//TraditionalForm

FullSimplify[
FibonacciQ[n+1].FibonacciQ[n]==FibonacciQ[2n+1],
n∈Integers]

(Q^m)(Q^(n-1))=(Q^(n+m-1))

FullSimplify[
FibonacciQ[m].FibonacciQ[n-1]==FibonacciQ[n+m-1],
(m|n)∈Integers]

MatrixForm@FibonacciQ[m].MatrixForm@FibonacciQ[n-1]==FibonacciQ[n+m-1]//TraditionalForm