# Factored form of basis

Originally for linear programming, this pertains to writing a basis $LaTeX: B$ in the form, $LaTeX: B = F_1 F_2 ... F_k$ , where $LaTeX: F_i$ are factors. Two forms of interest are: elementary factors, where each $LaTeX: F_i$ is an elementary matrix, and LU decomposition: $LaTeX: B=LU$, where $LaTeX: L$ is lower triangular and $LaTeX: U$ is upper triangular. ($LaTeX: L$ and $LaTeX: U$ might be factored, notably into elementary matrices, which are lower and upper triangular, resp.) These have inexpensive updates when $LaTeX: B$ changes to an adjacent basis.