R: Compute the Hilbert-Schmidt norm of a matrix

hilbert.schmidt.norm {matrixcalc} | R Documentation

## Compute the Hilbert-Schmidt norm of a matrix

### Description

This function returns the Hilbert-Schmidt norm of the matrix {\mathbf{x}}.

### Usage

    hilbert.schmidt.norm(x)

### Arguments

`x` | a numeric vector or matrix

### Details

The formula used to compute the norm is ≤ft\| {\bf{x}} \right\|_2. This is merely the entrywise norm with exponent 2.

### 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

`entrywise.norm`

### Examples

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

[Package matrixcalc version 1.0-3 Index]