Triangular Decomposition of a Matrix --- Generic Function
DESCRIPTION:
Computes triangular decompositions of matrices.

This function is generic (see Methods); method functions can be written to handle specific classes of data. Classes which already have methods for this function include: "Matrix", "Hermitian"

USAGE: 
lu(x, ...)
REQUIRED ARGUMENTS:
x:
a matrix. No missing values or IEEE special values are allowed.
OPTIONAL ARGUMENTS:
...:
additional arguments, such as choosing lower or upper triangular factors in the Hermitian case.
VALUE:
a representation of a triangular decomposition of x.
BACKGROUND:
If A is a matrix, then A = LU, where L is unit lower trapezoidal, and U is upper trapezoidal. At least one of L or U is triangular; both are triangular if A" is square.

If A is a Hermitian matrix, then A can be factored as L B t(L) or t(L) B L, where L is unit lower triangular, and B is block diagonal with either 1 by 1 or 2 by 2 diagonal blocks. If A is positive semi-definite, then B is diagonal, and this factorization is a variant of the Choleski decomposition.

REFERENCES:
Golub, G., and Van Loan, C. F. (1989). Matrix Computations, 2nd edition, Johns Hopkins, Baltimore.
SEE ALSO:
qr , chol
EXAMPLES: 
library(Matrix)
x <- Matrix( rnorm(9), 3, 3)
lu(x)