Norms and Related Functions for Matrices --- Generic Function

DESCRIPTION:

Computes a variety of matrix norms and related functions (e.g., the element of maximum modulus) for matrices. .LB Matrix

This function is an S Version 3 generic (see Methods); method functions can be written to handle specific S Version 3 classes of data. Classes which already have methods for this function include:
, , , , , . , .

USAGE:

norm(x, type) 

REQUIRED ARGUMENTS:

x
a matrix of class "Matrix" , or an object of class "eigen.Hermitian" or "svd.Matrix" . No missing values or IEEE special values are allowed.

OPTIONAL ARGUMENTS:

type
a value indicating the quantity to be computed. type is used only when x is a Matrix.

VALUE:

A numeric value representing the norm or related quantity.

BACKGROUND:

If A is a matrix, its one norm is the maximum l-1 norm of its columns, and its infinity norm is the maximum l-1 norm of it rows, its two norm is its largest singular value, and its Frobenius norm is its l-2 norm if the entire matrix were taken as a vector. Golub, G., and Van Loan, C. F. (1989). Matrix Computations, 2nd edition, Johns Hopkins, Baltimore.

SEE ALSO:

EXAMPLES:

library(Matrix) 
x <- Matrix( rnorm(9), 3, 3) 
norm(x, type = "1" )    # one-norm of x (maximum column sum)