Syntax of norm - What does 'Fro' mean?

(Frank) #1

In the manual, I found the following for the command “norm”:

⋆ norm: norms for real and complex vectors and matrices. Convex. The oneargument
version norm(x) computes the 2-norm for vectors and induced 2-norm
(maximum singular value) for matrices. The two-argument version norm(x,p)
is supported as follows:
– For vectors, all p ≥ 1 are accepted, but see Appendix D.2 for more details
about how cvx handles values other than 1, 2, and Inf.
– For matrices, p must be 1, 2, Inf, or ’Fro’.

So my question is - what does 'Fro" mean?

Many thanks!

(Mark L. Stone) #2

norm(X,‘fro’) is the Frobenius norm, that is sqrt(sum(diag(X’*X)))
which also equals norm(X(:)) = norm(X(:),2) , i.e., the square root of the sum of all squared elements in the matrix…

Note that as stated in the online help, you have to enter it as ‘fro’, not '‘Fro’…

(Frank) #3

Thank you so much for your prompt reply, Mark!