Frobenius Norm

The Frobenius norm, sometimes also called the Euclidean norm (which may cause confusion with the vector -norm which also sometimes known as the Euclidean 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"].

SEE ALSO:Hilbert-Schmidt Norm, Matrix Norm