What does the function 'norm' do?

Please tell me what does the 2(in bold) in the below expression mean?

residsumsq = norm(y-yhat, 2 )^2;

Also, Is the norm function referring to summation? I read the documentation but it is not clear.

Answer 1

[Walter Roberson]

norm

n = norm(X) returns the 2-norm of input X and is equivalent to norm(X,2). If X is a vector, this is equal to the Euclidean distance. If X is a matrix, this is equal to the largest singular value of X.

The 2-norm is equal to the Euclidean length of the vector.

So it norm(x) is norm(x,2) is sqrt(sum(x.^2))

Answer 2

[Bruno Pop-Stefanov]

The second input argument of the "norm" function specifies the order of the norm you would like to use. The default norm is the 2-norm, which is the Euclidean distance.

The p-norm is the p-th root of the sum of the terms elevated to the p-th power, i.e.:

http://en.wikipedia.org/wiki/Norm_(mathematics)#p-norm

[Priya]

Thank you. So, is it ok to write this way

 SS_res=∑(y-yhat,2)^2

[Walter Roberson]

No, it would be

SS_res = ∑(y-yhat)^2

There would normally be a sqrt() around the sum() but you then square the result of the norm, so that cancels out the sqrt()

[Priya]

Ya, I understood now. Thanks very much for your help.

Answer 3

[dpb]

It's the order of the norm requested, in this case the "2-norm" which is the same thing as the Euclidean norm...

http://lall.stanford.edu/svn/engr207c_2010_to_2011_autumn/data/norms_2008_10_07_01.pdf

[Priya]

Thank you.