Re: restrictions on parameters

• To: mathgroup at smc.vnet.net
• Subject: [mg31973] Re: restrictions on parameters
• From: "Allan Hayes" <hay at haystack.demon.co.uk>
• Date: Fri, 14 Dec 2001 16:53:01 -0500 (EST)
• References: <9vcgq9\$3js\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Thomas,
Yes, the restrictions need to be applied locally:

Clear[a,b,c,d]
restrictions={a<0,b>0,c>0,d>0};
A={{a,b},{c,d}};

eigen=Eigensystem[A];

det1=Det[A];

Simplify[det1<0, restrictions]

True

The same technique works on  the eigenvalues

Also note

Simplify[Sign[{eigen[[1]],det1}],restrictions]

{{-1,1},-1}

Allan

---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565

"Thomas Steger" <steger at uni-greifswald.de> wrote in message
news:9vcgq9\$3js\$1 at smc.vnet.net...
> 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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