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Re: Eigensystem ignoring assumptions

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$Assumptions is not used universally in all functions but rather in
functions specifically intended to use $Assumptions.

??$Assumptions

$Assumptions is the default setting for the Assumptions option used in such
functions as Simplify, Refine, and Integrate.  >>

$Assumptions=True


$Assumptions=b==0;

m1=({{a,b},{b,-a}});

Eigensystem[m1//Simplify]

{{-a,a},{{0,1},{1,0}}}


Bob Hanlon



On Thu, Jan 30, 2014 at 11:04 PM, Abced Def <ffcitatos@gmail.com> wrote:

>
> Hi,
>
> I am trying to understand, why Eigensystem is ignoring the assumptions and
> still dividing by something that is explicitly assumed to be zero. This is
> a more extreme counterpart of the b>=0 case. Any comments or references to
> the documentation are appreciated.
>
>
>
>
> In[320]:= Clear["Global`*"]
>
> In[321]:= $Assumptions = b == 0;
>
> In[322]:= m1 = ({
>     {a, b},
>     {b, -a}
>    });
>
> In[323]:= Eigensystem[m1]
>
> Out[323]= {{-Sqrt[a^2 + b^2], Sqrt[
>   a^2 + b^2]}, {{-((-a + Sqrt[a^2 + b^2])/b),
>    1}, {-((-a - Sqrt[a^2 + b^2])/b), 1}}}
>
>
>

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Re: Eigensystem ignoring assumptions Bob Hanlon <hanlonr357@gmail.com> - 2014-02-01 05:34 +0000

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