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. .LB Matrix

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:

,

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))