On Mon, Oct 22, 2012 at 10:00 AM, Jason Grout <jason-s...@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-s...@creativetrax.com <mailto:jason-s...@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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