= Majorization
{title2=$x\prec y$}
{wiki}
For real vectors of equal length and equal sum, write $x\prec y$ when $\sum_{j=1}^k x_j^\downarrow\leq\sum_{j=1}^k y_j^\downarrow$ for every proper initial segment; the downward arrow means decreasing rearrangement. Majorization compares how unevenly a fixed total is distributed. The uniform probability vector is majorized by every probability vector, while $(1,0,\ldots,0)$ majorizes every probability vector. The order controls exact pure-state entanglement conversion in <Nielsen's pure-state conversion theorem>.
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