# Factored form of basis

### From Glossary

Originally for linear programming, this pertains
to writing a basis in
the form, , where are *factors*. Two
forms of interest are: *elementary factors*, where each is
an elementary matrix, and LU decomposition:
, where is lower triangular and is upper triangular.
( and might be factored, notably into elementary matrices, which are
lower and upper triangular, resp.) These have inexpensive updates
when changes to an adjacent basis.