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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- Nov 18th 2010, 08:15 PMsouthprkfan1Positive 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. - Nov 19th 2010, 01:27 AMFernandoRevilla
Are there any hypothesis about $\displaystyle A$ ?

Regards.

Fernando Revilla - Nov 19th 2010, 12:08 PMsouthprkfan1
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.