| inf.norm {matrixcalc} | R Documentation |
Compute the infinitity norm of a matrix
Description
This function returns the \left\| {\mathbf{x}} \right\|_\infty norm of the matrix {\mathbf{x}}.
Usage
inf.norm(x)
Arguments
x |
a numeric vector or matrix |
Details
Let {\bf{x}} be an m \times n numeric matrix.
The formula used to compute the norm is
\left\| {\bf{x}} \right\|_\infty = \mathop {\max }\limits_{1 \le i \le m} \sum\limits_{j = 1}^n {\left| {x_{i,j} } \right|} .
This is merely the maximum absolute row sum of the m \times n maxtris.
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
Examples
A <- matrix( c( 3, 5, 7, 2, 6, 4, 0, 2, 8 ), nrow=3, ncol=3, byrow=TRUE )
print( inf.norm( A ) )