matrixcalc (version 1.0-6)

maximum.norm: Maximum norm of matrix

Description

This function returns the max norm of a real matrix.

Usage

maximum.norm(x)

Value

A numeric value.

Arguments

x

a numeric matrix or vector

Author

Frederick Novomestky

Details

Let \({\bf{x}}\) be an \(m \times n\) real matrix. The max norm returned is \(\left\| {\bf{x}} \right\|_{\max } = \mathop {\max }\limits_{i,j} \left| {x_{i,j} } \right|\).

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

inf.norm, one.norm

Examples

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