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Minkowski Inequality

Revision as of 01:23, 21 April 2008 by I like pie (talk | contribs)

The Minkowski Inequality states that if $r>s$ is a nonzero real number, then for any positive numbers $a_{ij}$, the following holds: $\left(\sum_{j=1}^{m}\left(\sum_{i=1}^{n}a_{ij}^r\right)^{s/r}\right)^{1/s}\geq \left(\sum_{i=1}^{n}\left(\sum_{j=1}^{m}a_{ij}^s\right)^{r/s}\right)^{1/r}$

Notice that if either $r$ or $s$ is zero, the inequality is equivalent to Holder's Inequality.

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