matrixcalc (version 1.0-3)

one.norm: Compute the one norm of a matrix

Description

This function returns the \(\left\| {\bf{x}} \right\|_1 \) norm of the matrix \({\mathbf{x}}\).

Usage

one.norm(x)

Arguments

x

a numeric vector or matrix

Value

A numeric value.

Details

Let \({\bf{x}}\) be an \(m \times n\) matrix. The formula used to compute the norm is \(\left\| {\bf{x}} \right\|_1 = \mathop {\max }\limits_{1 \le j \le n} \sum\limits_{i = 1}^m {\left| {x_{i,j} } \right|} \). This is merely the maximum absolute column sum of the \(m \times n\) maxtris.

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

Examples

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

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