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linalg(deprecated)

 fibonacci
 fibonacci matrix

 Calling Sequence fibonacci(n)

Parameters

 n - non-negative integer

Description

 • Important: The linalg package has been deprecated. Use the superseding packages, LinearAlgebra and VectorCalculus, instead.
 - For information on migrating linalg code to the new packages, see examples/LinearAlgebraMigration.
 • The fibonacci(n) calling sequence returns the nth fibonacci matrix, $F\left(n\right)$, defined as follows:

$F\left(0\right)=\mathrm{matrix}\left(1,1,\left[1\right]\right)$

$F\left(1\right)=\mathrm{matrix}\left(1,1,\left[1\right]\right)$

$F\left(2\right)=\mathrm{matrix}\left(2,2,\left[1,1,1,0\right]\right)$

$F\left(n\right)=[[F\left(n-1\right),F\left(n-1\right)],[F\left(n-1\right),0]],\mathrm{where}\mathrm{dim}F\left(n\right)=\mathrm{dim}F\left(n-1\right)+\mathrm{dim}F\left(n-2\right)$

 Note: Only the first $\mathrm{dim}\left(F\left(n-1\right)+\mathrm{dim}\left(F\left(n-2\right)\right)\right)$ rows and columns are retained.
 • The command with(linalg,fibonacci) allows the use of the abbreviated form of this command.

Examples

Important: The linalg package has been deprecated. Use the superseding packages, LinearAlgebra and VectorCalculus, instead.

 > $\mathrm{with}\left(\mathrm{linalg}\right):$
 > $\mathrm{fibonacci}\left(3\right)$
 $\left[\begin{array}{ccc}{1}& {1}& {1}\\ {1}& {0}& {1}\\ {1}& {1}& {0}\end{array}\right]$ (1)