Spectral Norm from Eigenvalue Decomposition

DESCRIPTION:

Computes the spectral (2) norm of a matrix given its singular-value decomposition. .LB Matrix

USAGE:

norm.svd.Matrix(x) 

REQUIRED ARGUMENTS:

x
An object of class "svd.Matrix" representing the singular value decomposition of a numeric or complex Matrix.

VALUE:

An object 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 of a matrix is equal to its largest singular value.

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) 
norm(svd(x))