Re: Eigensystem

• To: mathgroup at smc.vnet.net
• Subject: [mg73325] Re: [mg73309] Eigensystem
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Mon, 12 Feb 2007 05:04:14 -0500 (EST)

```Eigensystem will maintain the precision of the least precise input. If you want high precision give it high precision inputs.

m={{1,2},{3,4}};

es=Eigensystem[m];

t=Transpose[es[[2]]];

Simplify[m.t-t.DiagonalMatrix[es[[1]]]]

{{0, 0}, {0, 0}}

m={{Random[Real,{0,1},50],
Random[Real,{0,1},50]},
{Random[Real,{0,1},50],
Random[Real,{0,1},50]}};

es=Eigensystem[m];

t=Transpose[es[[2]]];

Simplify[m.t-t.DiagonalMatrix[es[[1]]]]

{{0``49.59034527615688, 0``49.83942922976429}, {0``49.58735034913213, 0``50.05028140987655}}

m={{Random[Real,{0,1},50],
Random[Real,{0,1},35]},
{Random[Real,{0,1},50],
Random[Real,{0,1},50]}};

es=Eigensystem[m];

t=Transpose[es[[2]]];

Simplify[m.t-t.DiagonalMatrix[es[[1]]]]

{{0``34.91939782420133, 0``35.16524293662837}, {0``34.59030012679873, 0``34.92880488167243}}

Bob Hanlon

>
>
>
> I am a user of Mathematica 5.2 for Windows.
>
> Please can you advice me how to run Eigensystem function so that its result
> has precision (say 50)
>
> that is much higher then the Machine Precision.
>
>
>
> Thank you
>
>
>
>
>
> NASA Ames Research Center
>
> Discovery and System Health Area
>
> Intelligent Systems Division
>
> Mail Stop 269-3
>
> Moffett Field, CA 94035-1000
>
> Tel.: 650-604-2261
>
> Fax: 650-604-4036

```

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