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Math Help - Positive definiteness

  1. #1
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    Positive definiteness

    Let X and Y be mx1 vectors such that:

    XX'-YY' = S is positive semi-definite.

    Let A be any mxm matrix, show that

    Z=(A-I)^2 * S is also positive semi-definite

    ....no idea where to begin.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by southprkfan1 View Post
    Let A be any mxm matrix, show that
    Are there any hypothesis about A ?

    Regards.

    Fernando Revilla
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  3. #3
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    Sorry all, I screwed up....Let this be a lesson not to skip steps.

    I have to show ASA' is Positive semi-definite, which is straightforward.

    I posted a new similar question if anyone interested.
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