Positive amd PositiveDefiniteQ

*To*: mathgroup at smc.vnet.net*Subject*: [mg113575] Positive amd PositiveDefiniteQ*From*: Jay <jaiezee at gmail.com>*Date*: Wed, 3 Nov 2010 02:54:58 -0500 (EST)

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!