Condition Number for Hermitian Matrices from Eigenvalues
DESCRIPTION:
Computes the reciprocal two-norm condition number for a real symmetric and complex Hermitian matrix from its eigenvalues.
USAGE: 
rcond.eigen.Hermitian(x)
REQUIRED ARGUMENTS:
x:
An object of class "eigen.Hermitian" representing the eigenvalue decomposition of a real symmetric or complex Hermitian matrix.
VALUE:
A numeric value of class "rcond", representing the reciprocal two norm condition number of the matrix underlying x. A copy of the call to "rcond" is returned as an attribute.
DETAILS:
The two-norm condition number of a symmetric or Hermitian matrix is the ratio of smallest magnitude eigenvalue to its largest magnitude eigenvalue. 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.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(eigen(x))