Determinant of a Hermitian Matrix from Triangular Factorization
DESCRIPTION:
Computes the determinant (or its logarithm) of a real symmetric or complex Hermitian Matrix given its symmetric indefinite factorization.
USAGE: 
det.lu.Hermitian(x, logarithm=T)
REQUIRED ARGUMENTS:
x:
An object of class "lu.Hermitian" representing the symmetric indefinite decomposition of a real symmetric or complex Hermitian matrix.
OPTIONAL ARGUMENTS:
logarithm:
a logical variable indicating whether or not the logarithm of the modulus of the determinant should be returned rather than the determinant itself. The default is to return the logarithm.
VALUE:
returns an object of class "det".
REFERENCES:
Golub, G., and Van Loan, C. F. (1989). Matrix Computations, 2nd edition, Johns Hopkins, Baltimore.
SEE ALSO:
det.object , det.Hermitian
EXAMPLES: 
x <- Matrix( sample(-3:3, size = 9, replace = T), nrow = 3, ncol = 3)
x[row(x) > col(x)] <- t(x)[row(x) > col(x)]  # construct symmetric matrix
class(x) <-  Matrix.class(x)
det(lu(x))