# Positive definiteness

• Nov 18th 2010, 08:15 PM
southprkfan1
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.
• Nov 19th 2010, 01:27 AM
FernandoRevilla
Quote:

Originally Posted by southprkfan1
Let A be any mxm matrix, show that

Are there any hypothesis about $A$ ?

Regards.

Fernando Revilla
• Nov 19th 2010, 12:08 PM
southprkfan1
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.