Elimination multiplier ($l_{ik}=a_{ik}^{(k-1)}/a_{kk}^{(k-1)}$)

For $i>k$, an elimination multiplier is the scalar $l_{ik}=a_{ik}^{(k-1)}/a_{kk}^{(k-1)}$ used in the elementary row operation $R_i\leftarrow R_i-l_{ik}{R}_k$. This creates a zero below the pivot element. The remaining entries change by $a_{ij}\leftarrow a_{ij}-l_{ik}{a}_{kj}$ for $j>k$. Storing these elimination multipliers gives the subdiagonal entries of $L$ in LU decomposition; later row interchanges must also reorder the already stored coefficients.