Re: MatrixPower problem

• To: mathgroup at smc.vnet.net
• Subject: [mg124146] Re: MatrixPower problem
• From: Dana DeLouis <dana2010 at me.com>
• Date: Wed, 11 Jan 2012 04:20:28 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```> P = {{0, 1/2, 0, 1/2, 0}, {1/2, 0, 1/3, 0, 0},
{0, 1/2, 0, 1/2, 0}, {1/2, 0, 1/3, 0, 0}, {0, 0, 1/3, 0, 1}}
//MatrixForm

Hi.  Just to give another option...

// Have each output use Matrix Form

\$Post = MatrixForm

// Then...

=
P={{0,1/2,0,1/2,0},{1/2,0,1/3,0,0},{0,1/2,0,1/2,0},{1/2,0,1/3,0,0},{0,0,1/3,0,1}}

<< Output using MatrixForm >>

// Now, turn it off:

\$Post =.

e1={1,0,0,0,0};

Limit[MatrixPower[P,k].e1,k->\[Infinity]]
{0,0,0,0,1}

= = = = = = = = = =
HTH  :>)
Dana DeLouis

On Jan 7, 5:29 am, p... at RQNNE.invalid (Per R=F8nne) wrote:
> I have defined the following matrix:
>
> P = {{0, 1/2, 0, 1/2, 0}, {1/2, 0, 1/3, 0, 0},
>        {0, 1/2, 0, 1/2, 0}, {1/2, 0, 1/3, 0, 0}, {0, 0, 1/3, 0, 1}}
>
> And the following vector:
>
> e1 = {1, 0, 0, 0, 0}
>
> I try to solve:
>
> Limit[MatrixPower[P, k].e1, k -> \[Infinity]]
>
> And get the correct result:
>
> Out[7] = {0, 0, 0, 0, 1}
>
> But if I write the first statement as:
>
> P = {{0, 1/2, 0, 1/2, 0}, {1/2, 0, 1/3, 0, 0},
>        {0, 1/2, 0, 1/2, 0}, {1/2, 0, 1/3, 0, 0}, {0, 0, 1/3, 0, 1}}
> //MatrixForm
>
> I will not only get a more readle Out-format of the matrix. My
> Mathematica 8.1 for Students will also deny to calculate what is
> demanded. It will just list
>
> Limit[MatrixPower[P, k].e1, k -> \[Infinity]]
>
> with P replaced with the contents of the 5*5 matrix.
>
> I simply don't understant why.
>
> The output I can be pasted as:
>
> At least I get the following output:
>
> Limit[MatrixPower[\!\(\*
> TagBox[
> RowBox[{"(", "", GridBox[{
> {"0",
> FractionBox["1", "2"], "0",
> FractionBox["1", "2"], "0"},
> {
> FractionBox["1", "2"], "0",
> FractionBox["1", "3"], "0", "0"},
> {"0",
> FractionBox["1", "2"], "0",
> FractionBox["1", "2"], "0"},
> {
> FractionBox["1", "2"], "0",
> FractionBox["1", "3"], "0", "0"},
> {"0", "0",
> FractionBox["1", "3"], "0", "1"}},
>
> GridBoxAlignment->{
>          "Columns" -> {{Center}}, "ColumnsIndexed" -> {},
>           "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
> GridBoxSpacings->{"Columns" -> {
> Offset[0.27999999999999997`], {
> Offset[0.7]},
> Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
> Offset[0.2], {
> Offset[0.4]},
> Offset[0.2]}, "RowsIndexed" -> {}}], "", ")"}],
> Function[BoxForm`e\$,
> MatrixForm[BoxForm`e\$]]]\), k].{1, 0, 0, 0, 0}, k -> \[Infinity]]
>
> --
> Per Erik R=F8nnehttp://www.RQNNE.dk
> Errare humanum est, sed in errore perseverare turpe

```

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