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MatrixPower problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg124064] MatrixPower problem
  • From: per at RQNNE.invalid (Per Rønne)
  • Date: Sat, 7 Jan 2012 05:24:40 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • Reply-to: spam at RQNNE.dk (Per Rønne)

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 Rønne
http://www.RQNNE.dk
Errare humanum est, sed in errore perseverare turpe



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