The Cauchy–Schwarz Inequality IV

The Cauchy-Schwarz inequality,

\displaystyle\sum_{i=1}^n{a_i^2}\sum_{i=1}^n{b_i^2} \geq \left(\sum_{i=1}^n{a_ib_i}\right)^2,

holds for any pair of lists of n numbers, {a_i} and {b_i}, for i=1,2,\ldots,n. I am about to discuss a fourth proof of the Cauchy-Schwarz inequality. I have previously presented a first, second and third proof.  The fourth proof involves some algebraic pyrotechnics where we measure the difference between the expressions on each side of the Cauchy-Schwarz inequality. Continue reading

Goolge Wave Invitations

If you have been late to the party with Google Wave, Lifehacker has a donation thread where kindhearted souls with an excess of Google Wave invitations offer them to all who are interested.  You are going to need an active account on Lifehacker to request an invitation from most people, which is not as easy as it might seem.  However, a few people just paste their email in their comment, so you can just email them directly without needing to comment on Lifehacker.  I was able to get an invitation for a friend using Lifehacker’s donation thread so it seems to work.

[Hat tip: Lifehacker]