R: Compute the infinitity norm of a matrix

inf.norm {matrixcalc} | R Documentation

## Compute the infinitity norm of a matrix

### Description

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

### Usage

    inf.norm(x)

### Arguments

`x` | a numeric vector or matrix

### Details

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

### Value

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.

### See Also

`one.norm`

### Examples

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

[Package matrixcalc version 1.0-3 Index]