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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