       Re: restrictions on parameter

• To: mathgroup at smc.vnet.net
• Subject: [mg31983] Re: [mg31954] restrictions on parameter
• From: BobHanlon at aol.com
• Date: Fri, 14 Dec 2001 16:53:18 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```In a message dated 12/14/01 5:49:04 AM, steve at smc.vnet.net writes:

>Thu, 13 Dec 2001 12:35:49 +0100
>From: Thomas Steger <thomas.steger at uni-greifswald.de>
To: mathgroup at smc.vnet.net
>To: mathgroup at smc.vnet.net
>Subject: [mg31983] [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
>

A = {{a,b},{c,d}};

TrueQ returns False unless the expression evaluates to True.  Use Simplify
with assumptions

Simplify[Det[A] < 0, {a<0,b>0,c>0,d>0}]

True

{d1, d2} = Eigensystem[A][];

Simplify[d1 < 0, {a<0,b>0,c>0,d>0}]

True

Bob Hanlon
Chantilly, VA  USA

```

• Prev by Date: Solved: Packed array generation and complex numbers
• Next by Date: RE: Bump Function
• Previous by thread: Solved: Packed array generation and complex numbers
• Next by thread: Eigenvalue Problem