frobenius.norm {matrixcalc}

Compute the Frobenius norm of a matrix

Description

This function returns the Frobenius norm of the matrix {\mathbf{x}}.

Usage

frobenius.norm(x)

Arguments

x

a numeric vector or matrix

Details

The formula used to compute the norm is \left\| {\bf{x}} \right\|_2. Note that this is the entrywise norm with exponent 2.

Value

A numeric value.

Author(s)

Frederick Novomestky [e-mail]

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( frobenius.norm( A ) )