Compute the entrywise norm of a matrix
This function returns the ≤ft\| {\bf{x}} \right\|_p norm of the matrix {\mathbf{x}}.
entrywise.norm(x,p)
x |
a numeric vector or matrix |
p |
a real value for the power |
Let {\bf{x}} be an m \times n numeric matrix. The formula used to compute the norm is ≤ft\| {\bf{x}} \right\|_p = ≤ft( {∑\limits_{i = 1}^m {∑\limits_{j = 1}^n {≤ft| {x_{i,j} } \right|^p } } } \right)^{{1 \mathord{≤ft/ {\vphantom {1 p}} \right. \kern-νlldelimiterspace} p}}.
A numeric value.
If argument x is not numeric, the function displays an error message and terminates. If argument x is neither a matrix nor a vector, the function displays an error message and terminates. If argument p is zero, the function displays an error message and terminates.
Frederick Novomestky fnovomes@poly.edu
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.
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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