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What's the difference between $\sigma_{uv}^2$ and $\sigma_{uv}$?

The covariance is defined as $\sigma^2_{uv} \equiv \langle (u-\bar{u})(v-\bar{v})\rangle$; my convention is to write it with $^2$. It's also often denoted $\rm {cov}(u,v)$ (which might actually be a somewhat less confusing notation), or sometimes $\sigma (u,v)$. (Presumably $\sigma_{uv}$ is the square root of the covariance.) I may have inadvertently dropped the $^2$ in lecture today for some instances...

Kate Scholberg 2014-11-10