Pivot element
= Pivot element
{title2=$a_{kk}^{(k-1)}$}
A <pivot element> is the current diagonal entry used to eliminate entries below it in <Gaussian elimination>, after any row interchange. At step $k$ it is $a_{kk}^{(k-1)}$, where $A^{(k-1)}$ is the current reduced <matrix>. Computing <elimination multipliers> requires this entry to be nonzero. A zero <pivot element> can reflect an unsuitable row order even for an <invertible matrix>, as <Pivoted LU decomposition> illustrates.