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        riddles >> medium >> positive definite
        
(Message started by: trusure on Apr 17th, 2010, 8:45pm)
Title: positive definite
Post by trusure on Apr 17th, 2010, 8:45pm
a function f(x) is positive definite if for every choice of finitely many si the mxm matrix (f(si-sj)), i,j=1,2,...,m is positive semi-definite.
Now my problem is to show whether its true that the function f(x-c) is also a positive definite or not, for an constant c??

I started by:
f((si-sj)- c)= f(si-sj-c)= f((si-c/2) - (sj+c/2)), and

I stopped here !?

any help
Title: Re: positive definite
Post by Obob on Apr 17th, 2010, 9:51pm
Try to find a counterexample.

The wikipedia page Positive-definite function (http://en.wikipedia.org/wiki/Positive-definite_function) is also useful.
Title: Re: positive definite
Post by trusure on Apr 18th, 2010, 7:57am
yes, I was thinking that it is not true for f(x-c) to be positive definite... I think I have an example in my mind I will check it.. thank you


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