Pivot element

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The pivot or pivot element is the element of a matrix, which is selected first by an algorithm (e.g. Gaussian elimination, Quicksort, Simplex algorithm), to do certain calculations with the matrix.

The above mentioned matrix algorithms require an entry distinct from zero in pivot position to work properly or at all respectively. Depending on the algorithm either one (random) element distinct from zero or the element with the greatest absolute value in a row or column is chosen. This is called pivotization. The row containing the pivot element is called pivot row, the pivot element's column is called pivot column.

Pivot element in Quicksort means the element that is selected as boundary for partitioning. Quicksort sorts all elements „left“ and „right“ of the pivot element recursively.