matrixcalc (version 1.0-3)

entrywise.norm: Compute the entrywise norm of a matrix

Description

This function returns the \(\left\| {\bf{x}} \right\|_p \) 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

Value

A numeric value.

Details

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

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

Run this code
# NOT RUN {
A <- matrix( c( 3, 5, 7, 2, 6, 4, 0, 2, 8 ), nrow=3, ncol=3, byrow=TRUE )
print( entrywise.norm( A, 2 ) )
# }

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