Condition Estimation for Hermitian Matrices from Triangular Decomposition
DESCRIPTION:
Computes an estimate of the reciprocal condition number for a real symmetric and complex Hermitian matrix from its symmetric indefinite decomposition.
USAGE: 
rcond.lu.Hermitian(x, normx)
REQUIRED ARGUMENTS:
x:
An object of class "rcond.lu.Hermitian" representing the symmetric indefinite decomposition real symmetric or complex Hermitian matrix.
OPTIONAL ARGUMENTS:
normx:
The one/infinity norm of the matrix for use in condition estimation. By default, it is assumed that the norm is available as an attribute of a, since the default for lu.Hermitian is to return one/infinity norm of the matrix as an attribute.
VALUE:
A numeric value of class "rcond", representing the reciprocal one or infinity norm condition estimate. A copy of the call to "rcond" is returned as an attribute.
DETAILS:
Based on the functions dsycon and zhecon from Lapack (Anderson et al. (1994)). The condition number of a square matrix is the product of the norm of that matrix and the norm of its inverse. Its values fall in the range [1, Inf), where a value of Inf would imply a singular matrix. A matrix is said to be ill-conditioned if its has a large condition number. Another way to view a condition number of a matrix is as a factor by which errors for solutions to systems of equations with that matrix as coefficient matrix can be multiplied. Condition numbers usually are estimated rather than computed exactly for reasons of efficiency.
REFERENCES:
Anderson, E., et al. (1994). LAPACK User's Guide, 2nd edition, SIAM, Philadelphia. Golub, G., and Van Loan, C. F. (1989). Matrix Computations, 2nd edition, Johns Hopkins, Baltimore.
SEE ALSO:
rcond.Matrix , rcond.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)
rcond(lu(x))