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Re: Positive amd PositiveDefiniteQ

  • To: mathgroup at smc.vnet.net
  • Subject: [mg113612] Re: Positive amd PositiveDefiniteQ
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Thu, 4 Nov 2010 04:01:50 -0500 (EST)

Read the help for Assuming

?? Assuming

Assuming[a > 0, Simplify[Positive[a]]]

True

Assuming[a > 0, Simplify[NonNegative[a]]]

True

m = {{a, 0, 0}, {0, a, 0}, {0, 0, a}};

Assuming[a > 0, And @@ Simplify[
   Thread[Eigenvalues[m] > 0]]]

True

PositiveDefiniteMatrixQ evaluates before the assumption can be applied and, at that time, the matrix is not explicitly positive definite. It is then too late to use the assumptions. This differs from functions like Positive that return unevaluated when given a symbolic input.


Bob Hanlon

---- Jay <jaiezee at gmail.com> wrote: 

=============
Just starting out with Mathematica, so have trouble with positives. Any 
help would be wonderful.

a) Is there a way to specify new domains, other than real, integer etc, 
in particular positive or non-negative?

b) why is the answer not "True" to the input statement:
	Assuming[a > 0, Positive[a]]
	and how can it be made to work for scalars and matrices?
	
c) why do I get the answer "False" to

 Assuming[a > 0, PositiveDefiniteMatrixQ[{{a, 0, 0}, {0, a, 0}, {0, 0, a}}]]

when it ought to be True? And how can the Mathematica answer be corrected?

Cheers!




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