# one.norm: Compute the one norm of a matrix In matrixcalc: Collection of functions for matrix calculations

## Description

This function returns the ≤ft\| {\bf{x}} \right\|_1 norm of the matrix {\mathbf{x}}.

## Usage

 1 one.norm(x) 

## Arguments

 x a numeric vector or matrix

## Details

Let {\bf{x}} be an m \times n matrix. The formula used to compute the norm is ≤ft\| {\bf{x}} \right\|_1 = \mathop {\max }\limits_{1 ≤ j ≤ n} ∑\limits_{i = 1}^m {≤ft| {x_{i,j} } \right|} . This is merely the maximum absolute column sum of the m \times n maxtris.

A numeric value.

## Author(s)

Frederick Novomestky fnovomes@poly.edu

## References

Bellman, R. (1987). Matrix Analysis, Second edition, Classics in Applied Mathematics, Society for Industrial and Applied Mathematics.

Golub, G. H. and C. F. Van Loan (1996). Matrix Computations, Third Edition, The John Hopkins University Press.

Horn, R. A. and C. R. Johnson (1985). Matrix Analysis, Cambridge University Press.

inf.norm
 1 2 A <- matrix( c( 3, 5, 7, 2, 6, 4, 0, 2, 8 ), nrow=3, ncol=3, byrow=TRUE ) one.norm( A )