Saturday, May 19, 2012

Old Emails

At times, it's interesting to read through your old emails to remember what you were doing on the same date.
In fact, a former coworker of mine started a startup TimeHop ( based on precisely that idea.

Going eight years back in time, I was thinking about Cauchy-Schwartz inequalities. Nowadays, I am having trouble remembering what they are.

Date: 19 May 2004 21:53:11 -0400 (EDT)
From: Aleksandr Yampolskiy
Subject: a simple inequality

I have a question regarding a simple inequality:

Let m>1 and X1, X2, ..., Xm > 0.
Then it's easy to show (by induction on m) that
(X1^2 + X2^2 + ... Xm^2) < (X1 + ... + Xm)^2.
E.g. it's obvious that (3^2 + 5^2) > (3+5)^2.

I was curious if this inequality is simply a special case of some
other general inequality. It feels very much like Cauchy-Shwartz, but
it isn't.

The reason I am asking is that I would rather just cite this fact as a
special case of such and such inequality rather than posting a trivial proof of
this in the paper.

Thanks for advice.



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