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.
Golub, G. H. and Van Loan, C. F. Matrix Computations, 3rd ed. Baltimore, MD: Johns Hopkins, 1996.Higham,
N. J. "Matrix Norms." §6.2 in Accuracy
and Stability of Numerical Algorithms. Philadelphia: Soc. Industrial and
Appl. Math., 1996.Horn, R. A. and Johnson, C. R. "Norms
for Vectors and Matrices." Ch. 5 in Matrix
Analysis. Cambridge, England: Cambridge University Press, 1990.
-norm),
is matrix norm of an 
matrix 
defined as the square root
of the sum of the absolute squares of its elements,
,
where 
is the conjugate transpose, i.e.,
is implemented as Norm[m,
"Frobenius"] and of a vector 
as Norm[v,
"Frobenius"].
