Comment #23 on issue 2225 by Vinzent.Steinberg: Enhancing Matrix Norm http://code.google.com/p/sympy/issues/detail?id=2225
The Frobenius is norm is a (numerically motivated) approximation of the hard to calculate 2-norm. So I'm not sure if it makes sense as a symbolical default.
I think we have to improve Max() before implementing some of the norms, because IIRC it only accepts two arguments currently.
mpmath already has the "easy" norms. In sympy, we could also implement the 2-norm, because we have eigenvalues.
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