# Block pivot

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Given a detached coefficient form, a pivot is performed on a nonsingular submatrix of nonbasic variables (rather than just one element). Suppose the detached coefficient form is partitioned into 2 row blocks and 5 column blocks (with the last column corresponding to the right-hand side):

$LaTeX: A = \left[ \begin{array}{ccccc} I & 0 & P & R & e \\ 0 & I & Q & S & f \end{array} \right].$
(Note: each $LaTeX: I$ is an identity matrix of appropriate dimension.) If $LaTeX: P$ is nonsingular, the basis can change by entering all (nonbasic) variables associated with the columns of $LaTeX: P$ for all basic variables associated with the rows of $LaTeX: P$.