# [Numpy-discussion] matrix norm

Charles R Harris charlesr.harris at gmail.com
Mon Oct 22 12:08:46 EDT 2012

```On Mon, Oct 22, 2012 at 10:00 AM, Jason Grout
<jason-sage at creativetrax.com>wrote:

> 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).
>
>
The 2-norm and the Frobenius norm are the same thing.

> "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."
>
>
OK, looks like Mathematica does return the induced (operator) norm. I
didn't see that bit.

Chuck
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