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
