Compute the Frobenius norm of a matrix
This function returns the Frobenius norm of the matrix {\mathbf{x}}.
frobenius.norm(x)
x |
a numeric vector or matrix |
The formula used to compute the norm is ≤ft\| {\bf{x}} \right\|_2. Note that this is the entrywise norm with exponent 2.
A numeric value.
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( frobenius.norm( A ) )
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