[Numpy-discussion] matrix norm

Jason Grout jason-sage at creativetrax.com
Mon Oct 22 12:00:22 EDT 2012

On 10/22/12 10:56 AM, Charles R Harris wrote:
> On Mon, Oct 22, 2012 at 9:44 AM, Jason Grout
> <jason-sage at creativetrax.com <mailto:jason-sage at creativetrax.com>> wrote:
>     I'm curious why scipy/numpy defaults to calculating the Frobenius norm
>     for matrices [1], when Matlab, Octave, and Mathematica all default to
>     calculating the induced 2-norm [2].  Is it solely because the Frobenius
>     norm is easier to calculate, or is there some other good mathematical
>     reason for doing things differently?
> Looks to me like Matlab, Octave, and Mathematica all default to the
> Frobenius norm .

Am I not reading their docs correctly?

* Matlab (http://www.mathworks.com/help/matlab/ref/norm.html).

"n = norm(X) is the same as n = norm(X,2)." (and "n = norm(X,2) returns 
the 2-norm of X.")

* Octave (http://www.network-theory.co.uk/docs/octave3/octave_198.html).

"Compute the p-norm of the matrix a. If the second argument is missing, 
p = 2 is assumed."

* Mathematica (http://reference.wolfram.com/mathematica/ref/Norm.html)

"For matrices, Norm[m] gives the maximum singular value of m."



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