Frobenius Norm
The Frobenius norm, sometimes also called the Euclidean norm (a term unfortunately also used for the vector 
-norm), is matrix
norm of an 
matrix 
defined as the
square root of the sum of the absolute squares of
its elements,
 |
(Golub and van Loan 1996, p. 55).
The Frobenius norm can also be considered as a vector norm.
It is also equal to the square root of the matrix trace of 
, where 
is the conjugate transpose, i.e.,
 |
The Frobenius norm of a matrix 
is implemented
as Norm[m,
"Frobenius"] and of a vector 
as Norm[v,
"Frobenius"].
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Anger J