Re:Sign of determinant

• To: mathgroup at smc.vnet.net
• Subject: [mg31991] Re:Sign of determinant
• From: Maryvonne Teissier <my.teissier at cybercable.fr>
• Date: Sun, 16 Dec 2001 03:44:25 -0500 (EST)
• References: <200112140921.EAA03577@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi, Thomas

Your question is not so simple, because a < 0 is a test ie not an
assumption,
and Mathematica works with Complex,
and Positive is not a domain for Element in Version 4.
and Assumptions seems work only for Integrate.

You are ready to experiment some experimental commands of Version 4
that does the job

Experimental`ImpliesRealQ[{ a<0 , b>0 , c>0 , d>0 } , Det[ { {a , b} , {c ,
d}} ] <  0 ],

If some one of the list  gives you a better answer, please let me know.,
because I try hard
to avoid the use of Experimental`ImpliesRealQ in this case, but without
success.

And, if there is no other way , lot of thanks, because until now, i built
for myself examples
to use Experimental`ImpliesRealQ, interesting but more difficult,
mathematically speaking.

Sincerly
Maryvonne Teissier.

>  Thu, 13 Dec 2001 12:35:49 +0100
> From: Thomas Steger <thomas.steger at uni-greifswald.de>
To: mathgroup at smc.vnet.net
> Subject: [mg31991] [mg31954] restrictions on parameter
>
> Dear list,
>
> here is a probably simple problem with mathematica.
> Greetings
> Thomas
>
> Example: Given the restrictions on the parameters as shown below, I
> would like to check the sign of the determinant or the eigenvalues of
> Matrix A. The problem seems to be that the restricions on the parameters
> are not properly specified.
>
> Clear[a, b, c, d]
> a < 0; b > 0; c > 0; d > 0;
> A = {{a, b}, {c, d}};
>
> eigen = Eigensystem[A];
> {d1, d2} = {eigen[[1, 1]], eigen[[1, 2]]};
>
> det1 = Det[A]
> -b c + a d
>
> TrueQ[det1 < 0]
> False
>
> This should be true!
>
> TrueQ[d1 < 0]
> False

```

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