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.