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What does norm(A-B) mean in Matlab?

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Hi everybody

In Matlab software, what does it mean? :

norm(A-B); A & B are vectors for example : A=[1 2 3] and B=[4 5 6]

or if we say Y=norm(A-B); then how is Y computed?

Thx, Best Regards
 

Re: A simple question

Hi,

Considering A=[1 2 3] and B=[4 5 6], then A-B=[1-4 2-5 3-6]=[-3 -3 -3]
then the norm (L2 norm) of A-B is Y=SQRT((-3)^2+ (-3)^2+(-3)^2)=3*SQRT(3).
Correct me if I am wrong.
RFCMOS
 

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    scholar_a

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Re: A simple question

yea thats right
in matlab when u use this syntax:
norm(A-B);
it returns max(svd(A-B));
and SVD(A-B) is Singular value decomposition of (A-B)
Note that:
norm(a-b)=max(svd(a-b))
 

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    scholar_a

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Re: A simple question

Norm depens on metric which is given in linear space. If metric is Euclidean (this case has been discussed in messages above) then the norm is counted as the square root of the sum of vector's coordinates in the 2nd power.

However, metric may be city-block, Mahalanobis, etc. Then norm will be expressed in another way.

In general, norm of given vector is the distance between the zero vector and the given vector (norm depends on metrics)

With respect,

Dmitrij
 

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