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Positive amd PositiveDefiniteQ


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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