norm - matrix norms

Calling Sequence

[y]=norm(x [,flag])

Parameters

• x : real or complex vector or matrix (full or sparse storage)
• flag : string (type of norm) (default value =2)

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 : maxi(sum(abs(x),'r')) ).

norm(x,'inf'),norm(x,%inf) : The infinity norm of x (the largest row sum : maxi(sum(abs(x),'c')) ).

norm(x,'fro') : Frobenius norm i.e. sqrt(sum(diag(x'*x)))

For vectors

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

norm(v) : =norm(v,2) : 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  dhnorm  h2norm  abs