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Topic: positive definite (Read 659 times) |
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trusure
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positive definite
« on: Apr 17th, 2010, 8:45pm » |
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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
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Obob
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Re: positive definite
« Reply #1 on: Apr 17th, 2010, 9:51pm » |
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Try to find a counterexample.
The wikipedia page Positive-definite function is also useful.
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| « Last Edit: Apr 17th, 2010, 9:51pm by Obob » |
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trusure
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Re: positive definite
« Reply #2 on: Apr 18th, 2010, 7:57am » |
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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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