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MathGroup Archive 2001

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Re: restrictions on parameter

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

In a message dated 12/14/01 5:49:04 AM, steve at writes:

>Thu, 13 Dec 2001 12:35:49 +0100
>From: Thomas Steger <thomas.steger at>
To: mathgroup at
>To: mathgroup at
>Subject: [mg31983] [mg31954] restrictions on parameter
>Dear list,
>here is a probably simple problem with mathematica.
>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]
>This should be true!
>TrueQ[d1 < 0]

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}]


{d1, d2} = Eigensystem[A][[1]];

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


Bob Hanlon
Chantilly, VA  USA

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