Spectral Norm for Hermitian Matrices

DESCRIPTION:

Computes the spectral (2) norm or a real symmetric or complex Hermitian matrix given its eigenvalue decomposition. .LB Matrix

USAGE:

norm.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 "norm" representing the spectral or 2 norm of the matrix underlying x . A copy of the call to "norm" is returned as an attribute.

DETAILS:

The spectral or 2 norm the matrix underlying x is equal to its eigenvalue of largest magnitude.

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) 
norm(eigen(x))