norm

Arguments

x

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

flag

string (type of norm) (default value =2)

y

norm

Description

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(v,p)

The l_p norm (sum(v(i)^p))^(1/p) .

norm(v), norm(v,2)

The l_2 norm

norm(v,'inf')

max(abs(v(i))).

Examples

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)

See Also

• h_norm — H-infinity norm
• dhnorm — discrete H-infinity norm
• h2norm — H2 norm of a continuous time proper dynamical system
• abs — absolute value, magnitude
• svd — singular value decomposition