FACTORED FORM OF BASIS

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