R: Compute the entrywise norm of a matrix

entrywise.norm {matrixcalc} | R Documentation

## Compute the entrywise norm of a matrix

### Description

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

### Usage

    entrywise.norm(x,p)

### Arguments

`x` | a numeric vector or matrix
`p` | a real value for the power

### Details

Let {\bf{x}} be an m \times n numeric matrix. The formula used to compute the norm is ≤ft\| {\bf{x}} \right\|_p = ≤ft( {∑\limits_{i = 1}^m {∑\limits_{j = 1}^n {≤ft| {x_{i,j} } \right|^p } } } \right)^{{1 \mathord{≤ft/ {\vphantom {1 p}} \right. \kern-νlldelimiterspace} p}}.

### Value

A numeric value.

### Note

If argument x is not numeric, the function displays an error message and terminates. If argument x is neither a matrix nor a vector, the function displays an error message and terminates. If argument p is zero, the function displays an error message and terminates.

### 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`, `inf.norm`

### Examples

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

[Package matrixcalc version 1.0-3 Index]