[Numpy-discussion] matrix norm
Warren Weckesser
warren.weckesser at enthought.com
Mon Oct 22 12:09:24 EDT 2012
On Mon, Oct 22, 2012 at 10:56 AM, Charles R Harris <
charlesr.harris at gmail.com> wrote:
>
>
> On Mon, Oct 22, 2012 at 9:44 AM, Jason Grout <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 .
>
Not octave:
octave-3.4.0:26> a = [1 2; 3 4]
a =
1 2
3 4
The default norm (for a 2x2 matrix) is the spectral norm:
octave-3.4.0:27> norm(a)
ans = 5.4650
octave-3.4.0:28> norm(a, 2)
ans = 5.4650
octave-3.4.0:29> svd(a)(1)
ans = 5.4650
not the Frobenius norm:
octave-3.4.0:30> norm(a, 'fro')
ans = 5.4772
octave-3.4.0:31> sqrt(sum(sum(a.**2)))
ans = 5.4772
Warren
> Chuck
>
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