Re: MatrixPower problem
- To: mathgroup at smc.vnet.net
- Subject: [mg124083] Re: MatrixPower problem
- From: David Bailey <dave at removedbailey.co.uk>
- Date: Sun, 8 Jan 2012 04:25:33 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <je96q1$j7o$1@smc.vnet.net>
On 07/01/2012 10:29, 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]] > The following expression is wrong: 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 To see what is wrong, type P//FullForm As you will see, the MatrixForm has become part of the expression contained in P! Instead write: 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}}; P//MatrixForm BTW, it is best to avoid variables that start with a capital letter, as these can clash with new definitions in later versions of Mathematica. David Bailey http://www.dbaileyconsultancy.co.uk