## Thursday, April 12, 2007

### Latex For Blogger

This is a neat plugin. And just to test it, here's the Johnson-Lindenstrauss Lemma:

For any $0 < \epsilon < 1$ and any integer n, let $k$ be a positive integer such that
$k \ge 4(\epsilon^2/2 - \epsilon^3/3)^{-1}\ln n$
Then for any set of points $V$ of n points in $R^d$, there exists a map $f : R^d \rightarrow R^k$ such that for all $u,v \in V$,
$(1-\epsilon)\|u - v\|^2 \le \|f(u) - f(v)\|^2 \le (1+\epsilon)\|u - v\|^2$