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Re: Define a matrix function with size as argument
*To*: mathgroup at smc.vnet.net
*Subject*: [mg71380] Re: Define a matrix function with size as argument
*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
*Date*: Thu, 16 Nov 2006 00:53:18 -0500 (EST)
*Organization*: The Open University, Milton Keynes, UK
*References*: <ejf10f$4pt$1@smc.vnet.net>
Simone Giannerini wrote:
> Dear all,
>
> I am quite new to Mathematica and I have the following problem I could
> not find track of both in the Forum and in the documentation.
> I need to define a matrix function with size of the matrix as an
> argument. The function produces a tridiagonal matrix:
>
> Q[w_] := MatrixForm[SparseArray[
> {i_, j_} /; Abs[i - j] <= 1 -> Which[i < j,
> a[i - 1]*(1 - (i - 1)/(2*w)), i > j,
> (a[-i + 2*w + 1]*(i - 1))/(2*w), i == j,
> (-(1 - (i - 1)/(2*w)))*a[i - 1] -
> (a[-i + 2*w + 1]*(i - 1))/(2*w) + 1],
> {2*w, 2*w}]]
>
>
> dum = Q[2]
>
> the problem is that dum is not recognized as a matrix so that
> operations like Inversion and the like do not work.
MatrixForm is a wrapper function for display only: do not use it within
your function definition.
Q[w_] := SparseArray[{i_, j_} /; Abs[i -
j] â?¤ 1 -> Which[i < j, a[i - 1]*(1 - (i - 1)/(2*w)), i > j, (
a[-i + 2*w + 1]*(i - 1))/(
2*w), i == j, (-(1 - (i - 1)/(2*w)))*a[i - 1] - (a[-i + 2*
w + 1]*(i - 1))/(2*w) + 1], {2*w, 2*w}]
dum = Q[2]
dum // MatrixForm
Inverse[dum]
The above expression work as expected.
Regards,
Jean-Marc
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