Scilab Function
Last update : April 1993
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) .
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norm(v): =norm(v,2) : l_2 norm
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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,