Euclidean norm

The Frobenius norm, sometimes also called the Euclidean norm (a term unfortunately also used for the vector L^2-norm), is matrix norm of an m×n matrix A defined as the square root of the sum of the absolute squares of its elements, left double bracketing bar A right double bracketing bar _F congruent sqrt( sum_(i = 1)^m sum_(j = 1)^n ( left bracketing bar a_(i j) right bracketing bar )^2) (Golub and van Loan 1996, p. 55). The Frobenius norm can also be considered as a vector norm.

Hilbert-Schmidt norm | matrix norm