pivot

The leading entry in a row that row operations use as an anchor to clear the column around it.

A pivot is a row's leading nonzero entry, used as the anchor for row operations that clear every other entry in its column — first the entries below it while building row echelon form, then the entries above it while pushing on to reduced row echelon form. Scaling a pivot's row so the pivot itself equals $1$ is the standard last step before clearing its column.