frobenius.norm: Compute the Frobenius norm of a matrix
In matrixcalc: Collection of Functions for Matrix Calculations
View source: R/frobenius.norm.R
frobenius.norm R Documentation
Compute the Frobenius norm of a matrix
Description
This function returns the Frobenius norm of the matrix {\mathbf{x}}.
Usage
frobenius.norm(x)
Arguments
x
a numeric vector or matrix
Details
The formula used to compute the norm is ≤ft\| {\bf{x}} \right\|_2.
Note that this is the entrywise norm with exponent 2.
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
entrywise.norm
Examples
A <- matrix( c( 3, 5, 7, 2, 6, 4, 0, 2, 8 ), nrow=3, ncol=3, byrow=TRUE )
print( frobenius.norm( A ) )
matrixcalc documentation built on Sept. 15, 2022, 1:05 a.m.
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View source: R/frobenius.norm.R
| frobenius.norm | R Documentation |
Compute the Frobenius norm of a matrix
Description
This function returns the Frobenius norm of the matrix {\mathbf{x}}.
Usage
frobenius.norm(x)
Arguments
x |
a numeric vector or matrix |
Details
The formula used to compute the norm is ≤ft\| {\bf{x}} \right\|_2. Note that this is the entrywise norm with exponent 2.
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
entrywise.norm
Examples
A <- matrix( c( 3, 5, 7, 2, 6, 4, 0, 2, 8 ), nrow=3, ncol=3, byrow=TRUE ) print( frobenius.norm( A ) )
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
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