norm

norms of a vector or a matrix

y = norm(x)
y = norm(x, normType)

x

vector or matrix of real or complex numbers (full or sparse storage)

normType

For a matrix x: a number among 1, 2, %inf, -%inf, or a word among "inf" (or "i") or "fro" (or "f").
For a vector x: any number or %inf, -%inf; or a word "inf" ("i"), "fro" ("f").

Default value = 2.

y

norm: single positive real number.

For matrices

norm(x): or norm(x,2) is the largest singular value of x (max(svd(x))).
norm(x,1): The l_1 norm x (the largest column sum : max(sum(abs(x),'r')) ).
norm(x,'inf'),norm(x,%inf): The infinity norm of x (the largest row sum : max(sum(abs(x),'c')) ).
norm(x,'fro'): Frobenius norm i.e. sqrt(sum(diag(x'*x))).

For vectors

norm([]) and norm([],p) return 0.

norm(x) and norm(x,p) return NaN if x contains NaNs.

A = [1,2,3];
norm(A,1)
norm(A,'inf')
A = [1,2;3,4]
max(svd(A)) - norm(A)

A = sparse([1 0 0 33 -1])
norm(A)