Dear Tim
This is generally true: it's the Cauchy-Schwartz inequality. See any good 1st yr undergrad analysis text e.g. Rudin RCA.
Mark
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Radiation Epidemiology Branch
National Cancer Institute
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On Aug 31, 2010, at 7:54 AM, "Mak, Timothy" <[log in to unmask]> wrote:
> Hi allstat,
>
> I would be really grateful if someone can show me a proof or disproof of the following:
>
> Suppose a and b are column vector of the same length and contains non-negative elements.
>
> Is it generally true that:
>
> a'ab'b >= a'ba'b
>
> ???
>
> This arises in a 2x2 matrix of the form:
>
> a'a a'b
> a'b b'b
>
> Is it true that this matrix's determinant is non-negative as long as a and b have non-negative elements?
>
> Thanks in advance,
>
> Tim
>
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