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