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Computing The LU Factorization Of A Matrix
 Syntax `[`L`,`U`] = lu(`X`)` `[`L`,`U`, `P`] = lu(`X`)` See Also qred , svd , schur

Description
Computes matrices L and U such that ```      X = L * U ```where X is a real, double-precision or complex square matrix . ``` ```L``` ```is a matrix with the same type and dimension as X. If the argument P is present, L is a lower triangular matrix with ones along the diagonal. If the argument P is not present, there is a permutation matrix `P` such that `P * L` is lower triangular with ones along the diagonal. ``` ```U``` ```is an upper triangular matrix with the same type and dimension as X. ``` ```P``` ```If the argument P is present, it is a permutation matrix and ```      P * X = L * U ```(Note that this equation can also be written as `X = (P' * X) * U` and `P'` corresponds to the permutation matrix mentioned for the case where the argument P is not present.)

Example
If you enter ```      x = {[1., .5], [.5, 1.]}      [l, u] = lu(x)      print l * u ``` O-Matrix will respond ```      {      [ 1 , .5 ]      [ .5 , 1 ]      } ``` which is equal to the matrix `x`. If you continue by entering ```      print l ``` O-Matrix will respond ```      {      [  1 , 0 ]      [ .5 , 1 ]      } ``` If you then enter ```      print u ``` O-Matrix will respond ```      {      [ 1 , .5 ]      [ 0 , .75 ]      } ```